If you can afford it, go an buy a Line 6 Pod XT Live or the classic Pod XT bean model and an Atomic amp. You'll have 95% of Edge's tones minus some of the specific stuff like Mysterious Ways, Numb, Fly, Shimmer, etc. I suggest the Live so that you can switch effects easily, but if you're just playing in your room, go with the bean model.
If you already have an amp, then you might want to think about bypassing the amp modeling in the pod b/c your amp is going to color your tone, especially a tube amp. The combination of "coloring" can sound like crap. That's the nice thing about the Atomic. Also if you get a crappy solid state amp they work pretty well too b/c they are crappy b/c they sound lifeless by themselves which is perfect to use in combination with the Pod.
As far as pedals, the Boss SD-1 or Tubscreamer 9 are the most common distortions used throughout Edge's career. He has also used the Big Muff, OS-2, Ampeg Scrambler, and the DM4. For delays go with either the Memory Man or the DL4 b/c they have the Mod Delay which is the key to Edge's sound. The MXR Dynacomp might be a good addition as well and a good clean booster of some sort (Boss FA1, Dod FX10, Sweet FA, Fulltone FatBoos, Katana Boost).