Radio Shack is fine, but the little parts are pretty expensive compared to what you can get elsewhere.
You want to start with a good Proto-Board like one of these. Then you’ll want a decent power supply (you can use batteries for now, but a nice 0-12v supply is a wonderful thing), a multimeter, and then go get a project book that has circuit diagrams in both shematic and prototype form. Have fun!
Radio Shack is good if you need something right now, but most of their stuff is hideously overpriced and they never seem to have every component you’ll need for a project - even simple ones. If you can’t find a good place to buy stuff locally (which is likely), try Mouser or Digi-Key.
You may also want to check out this site for a pretty basic electronics primer, along with some simple projects and a list of common components you’ll want to purchase.
They’re basically a children’s toy, but with 250 documented circuits you can make. Everything from radios to high voltage generators (that can kill a lightning bug ), to audio devices that go WOooOOOO WoooooOOOOOOhhhhhh WoOoooooOOOOOh!! (And more!)
No soldering just a big circuit board with spring connectors and enough wires to connect anything to anything.
Those taught me a lot when I was a kid…
Plus I built shortwave radio and “lie detector” kits from there among various and sundry other things, which did serve as crash courses in soldering.
This might help a bit with regard to chips and logic.
Only other thing I can add as for sources is my favorite, www.newark.com
They still carry some items but Radio Shacks in my area have gotten rid of a lot of their DIY electronics stuff. And the prices are rather luxurious–the place I go to sells dusty, somewhat-aged-but-still-new 1/4-watt resistors out of bulk bins for three cents each. At RS, a pack of five shiny ones in a plastic carded package will cost you $1. I would suggest that you look around in the largest nearby major cities to see if there isn’t an independent electronics-hobby shop.
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Jameco and Digi-Key are the darlings of those in the model railroad world who are heavily into electronics.
Do a google search for surplus electronics, and you’ll get places like Herbach & Rademan, who are aimed more towards hobbyists than the two I already mentioned.
If you live in or near a major metropolitan area, look in the yellow pages for electronic wholesalers (or suppliers). It’s always good to have one locally so you can go in and look. Indianapolis, where I used to live, had 3; Norfolk VA area, where I am now, has none.
I suggest you get some breadboards and a power supply to start. Some are available already integrated. Also, a decent set of tools, including wirewrap. Oh, and 2 or more volumes of the 1k+1 available circuits for any occasion type books.
Yes, Radio Shack has something called Electronic Sensor Lab. I bought one for my kids for Christmas. It’s pretty nice, though I wonder if I should have gotten a Snap Circuit instead.
Of course, for the more serious/advanced student, breadboarding is the way to go. You may also want to check out a book called 101 Solderless Breadboarding Projects by Delton T. Horn.