A starter digital electronics lab (we do not call them spare rooms or offices.. for science!) need not be overly expensive; you should invest in a few basic tools, and a good soldering iron. ebay and kijiji and local ads are your friend. We almost feel guilty about ordering from China, but when you can get (dubious quality) parts for sometimes 10% the price ..
Basic tools you will want:
Some nice to have tools:
Theres some basic parts you'll want to acquire .. things you will often need, and want in your parts box. Also, get a parts box or wall hanging kit of drawers.
Rule #1: don't throw things out at home anymore - not without taking them apart first. With a soldering iron, or maybe a heat gun (a heavy duty hairdrier from an electronics shop), or other tools, you can pull or desolder or melt pieces of damned near anything; with a heatgun and pliers, you can pretty much melt 50% of the parts and connectors off a PC motherboard, and I bet you've been through a few of those over the years. Heck, you can drop into a garage sale or computer shop and pick up old video cards or old mobo's dirt cheap, and melt off all kinds of goodies. But more to point, since thats a little hard core.. you break your exercise machine? I bet theres some sensors, or an LCD display panel, or some buttons, or some voltage regulators, something in there, that you can clip off, or desoler with a few minutes work.. valuable parts, to save you money, and its fun to do; you'll learn some physical design and get handy while you're at it. I'm a software guy by trade, so getting into the real world, pulling everything apart, is great. Also, it teaches the kids some valuable lessons – things are not disposable.. they're repairable!
I tend to suggest getting a few of each thing, too; you don't pick one up line driver/buffer chip, you bu a 2-pack, or get 3-4; you may kill one, but more than likely you'll need 2 in a project; what if you kill one, and still need 2? have 3 on tap :P Most of the basic parts are cheap, and you can get them online for pennies. I mean, a lot of basic ICs will run 20c, or can be gotten as free samples. Skip lunch out one day, and buy a pack of 40 ICs instead. Good times.