An EQ pedal can be handy at times, but it depends on the situation. I used to have a cheapo danelectro 7 band eq that I used, but I was doing gigs where the backline was provided and I wasn't using my own amp, so the eq came in handy to tweak the sound on an unfamiliar amp.
When I used the eq on my own amp I used it to cut the sound out, kind of a lo-fi sound so I could kick the main distortion sound back in.
Regarding the single stompboxes, they pretty much all come without an ac adapter. Most will take batteries but depending on the pedal they can eat through batteries in no time. Fuzz, distortion, overdrive etc will draw very little current, whereas delay and other modulation pedals can use a lot more.
A cheapo way of powering multiple pedals is a daisy chain power supply. I have one as a backup and it powers 5 pedals with no fuss (some pedals will be noisy using a daisy chain, others have better power supply filtering built in). I used a fairly cheap pedal multi supply that works fine, it powers 8 pedals at 9vdc and 1 at 12vdc, twas about 40 quid.
As I said before the multi effect might be a good entry point, more so if it comes with a power supply. That may lead on to using single stompboxes or a higher quality multi effects, but if you're anything like me you'll end up with 30+ single boxes..i'm a sucker for overdrives.
