I wouldnt be too prejudiced against IC's for todays circuits one uses two main things and that is op amps and 555 timer IC's. There are many circuits one can build around these two devices, and what is really nice about IC's is one can replace them without too much hassel if you use IC sockets!
I designed a PCB for a dual op amp, that facilitates 20 different circuits. The op amp is a simple little device, for instance if you want an amp with a gain of 10 you will need 3 resistors and two caps. The gain is determined by the ratio of two of the resistors. One gets a "Power op amp" (TDA2003) that 4 resistors and 4 caps. One will have to scrounge around the websites for circuit diagrams, but if you get stuck contact me, I can email you diagrams, and pcb layouts too if need be.
The very first thing you should be building is a variable power supply, once you have that done you now have a power source to test anything else you want to build.