Johnnyboi, if you don’t yet own a microphone, does this mean that you haven’t been playing live before now? Or maybe your live setup is just for personal enjoyment? If so, I’d hold off thinking about effects until you take care of first things first. Yes, the SM57 or SM58 is a fine workhorse mike for just about anything.
Jem, I’d separate reverb and compression from other effects. Many live or recording setups use some reverb to compensate for room acoustics if needed, and some compression to balance an instrument’s presence in the mix if needed. It’s part of the overall sonic tailoring in any good audio technician’s kit.
Having individual control of your line reverb apart from the overall desk mix can be a good thing. Whistle responds quite differently from, say, guitar. And given the 30+ dB difference between low and high notes on many whistles, a little compression can make life easier - though it’s no substitute for learning how to work the microphone.
Of course, any effect can be abused, including intentionally for fun.
You always wanted to play your whistle in an empty Notre Dame, or inside a sewer pipe? Have at it! Compress your whistle attack to sound like an organ pipe. IMO, screwing around with effects in private is a great way to get it out of your system, and learn from experience where to set the dividing line between good taste and bad.
For most live performance, standard stomp boxes are practical and probably fine. Just chain together what you want. A Lexicon rack unit is definitely magical, but probably overkill. Another option is a software processor. Load it on a laptop for live use, and feed it via the FX send on your sub-mixer. Lots of flexibility.
Or, as mentioned, there’s something like the Behringer Xenyx 1002FX board, with 50 different reverb presets, as a sub-mixer. The preamps work well with an SM57, and you get lots of individual control over your EQ and level in the mix. The FX quality is comparable to a stomp box. No compressor, though; that’s a separate unit.
Behringer … I know about the bad rap for cheap quality control. But I’ve used a Xenyx 802 mini mixer and Behringer active DI box for a few years now. They’ve both been solid performers for me, and great values at the price. I can imagine problems in rock band situations where the gear gets manhandled and needs to be more robust. But with some extra care (and luck), it seems fine for personal or occasional live use. The DI is a bit noisy, but the Xenyx board is very quiet and A-OK, and small enough to slip right into my gig bag.