Here's a take from A NON EXPERT.
There are 3 gizmos that are relevant.
2 of them are delays. You buy two delays (that is, two of the same product) and set one to eighths and the other to dotted eighths.
The other is some kind of effects pedal, but that is a more complicated question because Edge uses different effects for different songs. I recall his first pedal was a Memory Man, so that should probably cover the 80s catalog.
As a non expert, I don't believe the guitar is important for approximating the sound on a basic/budget level - just something decent enough. Same with the amp, you'll want to be happy but an amp won't turn your playing into The Edge, it's the delay and pedal that are the key.
That's what I have gathered, anyway. I have never touched a delay or pedal in my life, and I (sniff) sold my guitar and amp a long time ago.