The multieffects boxes are good for that - a pretty convenient and cheap way to play with tons of effects. I really liked the Zoom effects processors I had for that.
In the end I went all stompbox too (mostly because I didn’t like digital overdrives and distortions so much.)
However, digital does just fine for lots of effects. Digital reverbs and delays are actually better than analog IMO (and in fact some of the best pedals are digital), and digital does fine for compression and some of the modulation effects too. So if you wanted to try a multi-effects box it would not be a waste of time at all 
We have a thread on the Zoom units here: