there's a lot of people on this thread saying oh you need this and you need that etc. here's what you NEED...
1. A meter. You don't need the best unit on the market, but stay away from the bottom of the barrel too. Most meters in the 30-50 dollar range will get you going.
2. You'll need a prototyping board. One of the 600 hole boards will be more than adequate, and if you shop around you should be able to find one for under 20 dollars.
3. A soldering station with a few chisel tips of various sizes. You can find old analog weller stations for a song on fleabay. We're talking easily under 50 dollars. They're built like the proverbial brick dunny, and even the used ones should last you the better part of 20 years. You don't need the latest and greatest digital unit with the bells and whistles.
4. Solder wick is nice for a lot of things but it's a consumable and a decent sub 10 dollar spring loaded sucker will do you fine to start out.
5. Get a 1 lb roll of 63/37 solder. 0.031" diameter(i think is the size) is good general purpose solder. You'll go through plenty of it so don't bother with smaller spools.
6. Get your hands on an assortment of phillips and flat tip screwdrivers in large and small sizes, needle nose pliers, a nut driver or socket wrench set, jewelers screwdrivers, and some decent side cutters. Again, you don't need the best in the world, just avoid the really cheap tools. Flea markets and yard sales are great for getting this stuff really inexpensively.
7. Go dumpster diving and start cannibalizing junk equipment for parts, bulk wire, and circuit boards to practice your soldering and desoldering skills on. Once you've accumulated a good collection you can build whatever else you may need like rudimentary power supplies and signal generators with the parts you've scored.
Scopes and function generators, and things like that are nice to have but they're luxuries if you're just starting out and you're not even sure you'll still be excited about the hobby in 6 months to a year from now. What I outlined above will get you up and running with a minimum outlay.