Going software means you have to bring a laptop whenever there's a gig, sure you wanna do that?
Can you switch multiple effects in stompbox or multieffect with one button ? Or is it one button - one effect ?
Multi : There are some multi units that has the "one switch one effect" feature. Boss GT6B for example, you can assign each pedal to turn on/off a specific effect, making it acts stompbox-like (usually they call it "manual mode"). Or you can assign several effects in a patch bank and turn them on/off at the same time.
Stompbox : You can turn on/off several fx unit at the same time using loopers, but things can get quite complicated down the road.
My advice is to start simple, check what you need for the songs, build your arsenal along the way. Take it slow, as this is a journey