Here's a good TI reference on building simple single-supply (as in 9V battery) opamp circuits, tackle this after you've understood that car audio page (I love that thing with its interactive circuits):
http://www.eng.yale.edu/ee-labs/morse/compo/sloa058.pdf
As for your projects, set aside EQ for the time being, those circuits can get quite involved. A mic pre is a good start, and a simple opamp-based mic pre is not too difficult.
A mic pre circuit will have three basic functions: phantom power supply, differential input, gain control/output (which can be the same amp stage).
The question is how you would like to power your circuits: 9Vs are great for guitar pedals but inadequate for mic amps. The amp itself will run OK on 9V (with limited headroom), but not many people like 9V for phantom power. Even so, building a mic amp with 9V (or better 2x 9Vs, then you have +/-9V and reasonable headroom) on breadboard is a good start to understanding how circuits work.
If you haven't already, buy a breadboard and a multimeter:
That one is probably twice the size you need.
You need to built a proper power supply ultimately, which means wall power, and that can be a little intimidating. Just remember that once the voltage comes off the secondary of the transformer, it is low voltage and won't kill you. So wire up the primary carefully, include a fuse or breaker, and make sure not to leave 120VAC leads exposed (use wirenuts, heatshrink, whatever)
A mic preamp will usually have three power rails: +48V for phantom and +/-15V (or higher) for the amps themselves. That can be a bit much to construct at first, but there are plenty of kits you can buy that do that--I think JLM sells one, and I know fivefish does.