I found plans for making wood boxes for shelves for storage that I liked at Family Handyman. Basically it’s a double box so it’s sturdier and I like that idea. In the plans they tell you to cut your wood about 1/8th inch bigger than you need and then rout off the overhang until both boxes are flush. Well, I am not very handy but I’ve got some power tools and I want to be handy but I don’t know a lot about the functions of different tools and I don’t want to buy another tool if i don’t have to. I do have a Dremel and I know they have routing bits for it and I wouldn’t mind buying new bits. But would that be good enough for this purposes?
Why don’t you want to buy another tool? I’ve never heard of that before 
Yes, the routing add-on for the dremel will work just fine, I love mine. The only thing is your had has to be steady as the face of the router attachment is only about 2 inches in diameter. Where if you were using a proper router, you could rest part of it on a level surface for accuracy. But you should be fine with the router attachment, it comes with 2,3 bits that should work.
I was going to suggest, if you were willing to purchase another tool, that you get a small hand planer. I’ve used my planers in lieu of routing several times, but then I have a series of planers that give me some versatility.
Well, I would just buy another tool if money weren’t an issue but a router is a bit more expensive than the bits for a tool I do own. If I find that I like building these boxes I may eventually buy a tool to make it easier. I want a lot of storage and I like the idea of building boxes to the size and purpose I want. I’ll look into a hand planer too, it might be an option.
I was kidding you a bit, I am someone who scours yard sales, thrift shops and the like for more tools… 
Basically, none of what I have is brand new, I’m a bit of a tool-aholic.
Craftsman has a few light duty routers for under $100. There’s no reason to spend $300 for a Porter Cable if you don’t need it.
How big are the boxes? How many are you making? A Dremel router bit works OK for the small stuff, but it’s not really designed for taking down a lot of stock in any reasonable amount of time. And I don’t think they’re carbide tipped (may be wrong about that), so they’ll probably get dull pretty fast.
A router is one of the more useful tools if you’re going to get serious about woodworking, so it’s not a bad investment. The bits are expensive, but you can often find them on sale at the woodworking stores (e.g. Woodcraft/Rockler).
I wouldn’t use a Dremel on any wood thicker than 1/4" or maybe 3/8"- it might get through 3/4" but it will take a while and you’ll probably get burning on the cut edge. Also, a Dremel is lightweight, which makes it somewhat less stable than a heavier router. I love my Dremel for certain jobs- sometimes it’s the only thing that will do the job, and in those situations they’re indispensable.
But I find a router to be a much more universally useful tool, and probably the right one for what you want to do.
Okay, here’s the project.
The size is customizable. I’ve been looking at a lot of instructions for cubes and rectangular boxes and I like these plans because they look sturdier. I might use some for books, I hate when bookshelves get saggy. Anyway, I’d probably start with some cubes to see how it works out. I’d like to hang them on the wall but I may stack others. I know I can buy pre-made cubes and cubbies but I can’t get them to the exact size I want, they get saggy and they’re made with that crappy particle board then eventually disintegrates.
For that project you’ll need a proper router and a flush-trim bit. The bit has a little ball bearing that rides along the side of the workpiece to guide your cut. Without that type of bit, you haven’t got a chance of doing a neat job; you won’t be able to guide a Dremel straight enough by hand. And a Dremel doesn’t have the power to run a flush-trim router bit.
In the page you linked, Step 3 Photo 4 shows a flush-trim bit being used.
Hmm, okay, I might look into Philosophr’s suggestion of a thrift store first. It is getting to be Christmas time and I usually buy myself a nice gift. My power tool set was a gift from myself a few years ago.
The other reason this project appeals to me is the bit about not having to be too fussy with the measurements, since one reason I keep putting this off is I’m afraid messing up the measurements/cuts.
Don’t forget pawn shops. There are deals to be had if you go in knowing the value of what you want to buy.
If you are able to keep the overhang to what they recommend, that 1/8", you can probably get away with a laminate trimmer. Get a bit with the bearing on the end and little round over bit.
This, plus you’ll find a router table *immensely *helpful for keeping a straight and even line. I got a used Black & Decker w/ bits from an ad on craigslist for $30 a couple years ago. Always check CL for tools…but make sure they work.
Well, you could actually use a Dremel straight bit if you tipped the box on the side and used a straight bit set to just graze the surface of the box. But it would take forever and plywood would dull the blade hopelessly in a couple of minutes.
You’ll wear out Dremel bits pretty quick. They seem to assume you can’t cut the pieces to right size and you’ll leave the excess on the back. I don’t know, but this sounds like the hard way to make simple boxes. I’d use pine boards, or edge glued panels, in width I wanted, cut the pieces to length, and use plywood only on the back. If you’re mounting this on the wall, the wall better be pretty flat, or you’ll have to mold around it anyway. You should be able to do all this with a handsaw and sandpaper.
TriPolar has the answer I was going to give after looking at the project website.
Why cut a board 1/8" too long on either side just to rout it flush when you could cut it to size? Or at the very most, just a hair over, and then sand it flush? And using plywood for the whole box may help ensure you don’t have warped boards to deal with at any point, but you’ll get a better-looking piece out of plain pine boards. A few extra minutes picking your lumber will get you straight pieces off the rack at Home Depot or wherever. And birch-veneered plywood isn’t cheap stuff - pine would save you money too. Not to mention not having to worry about chipping or tearing the veneer on your plywood when you cut it.
That said, I can say that a router is a much more versatile tool than I expected. If you get one, get a plunge router. I’ve got one of those and a table-mounted router, but the plunge is the more useful. I’ve got a little plunge router-style gadget (thanks again for the tip on that, guys) for my Dremel that’s good for very small stuff (like inlay) but wouldn’t be appropriate for this box project.
I went to a pawn shop and they had a Black & Decker fir $50 but it didn’t come with any bits and I don’t know enough to tell if it was a fixed base or plunge. I went to Lowes to get an idea of prices and they had a fixed base for $58, I forget the brand, again no bits included. Since I wasn’t sure if I wanted a fixed base or plunge I decided to do more research.
It sounds like I should go with a fixed base for what I want to do and for other projects I might want to do in the future. Reading about what plunges can do I just can’t see myself getting that involved. However I did check out the combo’s as a possibility but I was hoping to keep it under $100 and it seems the only way I can do that is with a refurbished model.
Looked at the project, gosh Wile E., if it were me I would use sand paper and a sanding block to round the edges off. Then again, do you or family plan on any future woodworking that might require router? If so, I would invest in one. The dremel is cheesy for doing routing work, imo.
I have a makita and black & decker router, would recommend makita. The porter cable routers are just too damn heavy, and not that great either, imo.
edited to add: don’t plunge style routers also bolt down, can then also be used as a fixed base type?
Plunge routers should all have a “lock” feature that holds the thing in one spot. Thats why I’d recommend anyone’s first router be a plunge. You can do almost anything a fixed can do, plus the stuff that a plunge is good for.
I guess it depends upon your goals.
If you just want to bang out a few boxes on the cheap then you don’t need a router. You should be able to accomplish this with a saw and sandpaper wrapped around a block. Make your cuts as accurately as you can and then sand back any excess instead of routing. Even better, batch the parts that need to be the same size (for example the top and bottom) and cut them together so you don’t have to fiddle with any measuring at all.
If you’re thinking about taking up woodworking as a hobby (and like to use machines and power tools) then by all means get a router. They’re a wonderfully versatile tool and nearly essential for building using modern power tool methods. If you only have one router, a plunge base would be the most useful. It’ll do everything a fixed base does, with the welcome addition of being able to start a cut in the middle of the board much more safely and accurately. A basic bit set will get you started, but you’ll need a flush trim bit with the bearing on the bottom for the specific task in the plans you linked. These generally aren’t sold with the routers, so you’ll have to buy them separately. If you’re going to buy a router (and you don’t need one for this project (see above)) then buy a good one. There are few things more frustrating than crappy tools.
If you’re thinking about taking up woodworking as a hobby and not necessarily wild about donning hearing protection against earsplitting noise and wearing a mask amidst clouds of sawdust and risking loss of fingers from spinning blades then there may be another path for you. There are quite a few of us using traditional hand tools like saws, planes and chisels instead of power tools like routers, circular saws and sanders. It lends itself (IMHO) to a more serene, artisanal approach. And it’s way more fun. Elegant weapons from a more civilized age.