Hey, at least it’s only homely oak, and not pernambuco or gaboon ebony.
You know, this thing looked… smaller before. I had optimistically hoped to have it mostly done, as in DONE, by Monday. As of now, Saturday night, I have sanded the top and mostly one side. Doing the vertical parts is much, much harder than I imagined. I am a slight, bird-boned girl. My arm may yet fall off. The varnish may prove tougher than I.
Are you able to turn it on its sides? Sanding horizontal surfaces is much easier than vertical ones.
Even if I was strong enough to turn it on its side, I’m not sure I’d be tall enough to sand it that way!
Oh, another question - should I be really worried about what I’m breathing in? I started out with a dust mask, but it was fogging up my safety goggles, which I felt were more important, and also there didn’t seem to be a ton of dust that wasn’t picked up by the sander into its little bag. (I have not tried attaching a shop vac, although I can.) When I started doing the vertical surface there was more loose dust, however. I understand that any small particulate can be harmful to the lungs, I’m asking more about the finish (and any other finish I might encounter).
Wood dust is dangerous – it’s a known carcinogen. The kind of fine dust produced by power sanding is more dangerous, because it’s more likely to get past your mask. It’s a question of dosage, though, and unless you plan to spend the rest of your life sanding (perish the though!), you’re probably okay with a simple dust mask. I tend to wear a respirator with replaceable cartridges like this. These kinds of masks are nice because with a separate filter, they can give you some protection against solvent fumes, and not just particulates. It’s worth knowing that some woods produce much more irritating or allergenic dust. Tropical hardwoods tend to be particularly bad – some even produce contact dermatitis, such that you should protect any exposed skin from the dust.
And don’t be surprised it’s taking longer than you thought. Just wait till you start putting the finish on! Weeks will pass.
Does breathing in a mask like that fog your safety glasses?
Okay, so I found some veneer on the thing, on the end-grain of the pieces that divide the doors/drawers. Besides being careful about the edges, is there anything else I need to know about sanding veneer? Also, in one place there’s a chip of veneer coming loose - it’s all there, but a bit is unglued. Can I fix that?
No problem. Just sand carefully, because it’s easy to go through the veneer. And yeah, just glue the loose chip down with yellow glue or Elmer’s.
As to the fogging issue, I just wear my normal everyday glasses when sanding, and I don’t have a problem fogging with that kind of mask.
How’s the airflow? I hate the dust mask because it feels suffocating, but then again when I blew my nose last night it was, you know, wood grain. Ugh.
Wear the dust mask. If you have to breathe with your mouth open, change the mask. In fact, change it just before that. 
I usually don’t use a respirator like the one linked above unless I’m working with exotics, but some domestic woods are also known to cause problems. Oak is usually safe, walnut bothers some people. I don’t have a list handy, though.
The piece in your picture looks like a credenza or a return for a desk. A friend of mine bought a similar piece at a used office furniture place and refinished it. He used colored polyurethane stains on his. The woodgrain still shows through, but the desk is a very dark red on top and a dark green on the sides. It’s not a combination I would have considered, but it looks very nice.
I am sitting at a desk that I bought at a used office supply store. It looks to me to be from the late '50’s or early '60’s and had the original varnish over what could be mahogany or similar dark dense wood. I used lots of stripper, and lots of sandpaper to get it back to bare wood, then finished it with nothing but linseed oil and paste wax. It is beautiful and I got it for $39. I think I paid more than that for all the stripper and sandpaper!
It’s a lot of fun to take something old, but well made and make it all new and pretty again. Good luck with your projects.
(I am not an expert on furniture refinishing.)
I see I’m too late to advise against sanding. Unless there are deep gouges, I would have started with mineral spirits (depending on the finish) and just wipe it on all over. It might re-dissolve the existing finish and result in a nice smooth surface.
I generally prefer a natural finish on wood furniture. Can’t tell what species it is, but I probably wouldn’t paint it. However, if you choose to go that route, sand the hell out of it, fill the pores, and enamel your heart away.
Wish you’d said that before I spent a couple days calling the piece “Asshole”. 
I think I’ll actually finish the sanding tonight.
Normally, I’d rather respect the wood and do a natural finish, but I wanted to try something different. (Plus, I didn’t really want to end up with the same piece of furniture I started with, because I don’t like that piece.) If it’s a total ugly-ass failure, it’s a $12 boondoggle.
Am I supposed to be running through the sanding sheets this fast, by the way? It seems like I’m just burning through them like crazy, and they’re hardly free!
If you’re just going to paint the piece, you don’t need to spend so much time sanding it. Just enough to give the existing finish some “tooth” for the paint to stick to, and to smooth out any big scrapes or gouges.
If you’re looking to take the thing down to bare wood and start fresh - egads, you could have picked something smaller to start with as your first project. 
At least you went with an item with a lot of flat surfaces, simple lines and uncomplicated details.
I recently freshened up a sad, tattered 20 year old blond oak bathroom vanity by scuff-sanding it, then giving it three coats of a tinted varnish. (IIRC, it was one of Minwax’s Polyshades finishes) It’s not perfect, and it’s not one of my prouder works, (Success with brushed clear finishes eludes me - I’m much more a fan of anything that’s hand-rubbed like Danish oil or whatever kind of wiping varnish I used on the fireplace mantel a few years ago) but for ten bucks worth of varnish, and knowing that the cabinet is going to be replaced completely in a year or two, it came out well.