A lot of your sound is determined by your amp. For instance I love overdrive pedals, and so does the Edge, but overdrive pedals tend to suck on transistor amps. But they sound lurvey on valve amps.
The Line6 DM4 is a good first buy as it gives you 16 kinds of overdrive, distortion and fuzz. There are bound to be a few useful sounds in there. It also has a built in noisegate. Separately the Boss OD-3 and SD-1 make for good overdrive pedals. The venerable Ibanez TS-9 tubescreamer is still the king of OD pedals but it's pricy. Since the Boss SD-1 shares almost the same PCB board as the TS-9 and if soldering doesn't frighten you you can modify it and get the same sound at half the price.
Distortions are much harder to please with. Both the Boss DS-1 and Electro-Harmonix Big Muff are widespread but I've never been a fan of either of them. The Proco Rat is also a classic. What these three have in common is that if soldering doesn't frighten you, you can find tons of mods on the internet to turn these basic pedals in boutique monsters. Which is basically what the manufacturers of boutique pedals do. Take a basic mass produced pedal, remove some cheap electronic components, install some better components and then sell it to you under a fancy name at over two to three times the cost.
Delays are a world of their own. I find that the Line6 Echo Park makes for a good alround starter. Whichever you choose, go for one that has tap tempo. Nothing sucks more then having to dial in the right delay tempo when it absolutely has to be in sync 100% like with a song like Streets.
And that still leaves you short stuff like wah, compressors, modulation, pitchshift. Which is why a multi effect like the Line6 Pod XT Live, or the Boss GT8 is still the best value for money. For the price of a few good separate pedals you get a full selection of effects all in one handy floor unit. The downside of course is that you'll have to learn how to program the damn thing. Which is nowhere as near as difficult as it sounds, but still takes a learning curve to get good sounds from it.