I would second Way of the Four Elements Monk. Magic initiate as a feat at 4 would let you pick up shape water, ray of frost, and plenty of options as a level 1 spell (fog cloud, frost fingers, ice knife, etc). Shape Water plus Shape of the Flowing River together will give you a TON of creative options.

A classic issue with Wot4E is that it burns through Ki points, which you also want for the usual monk things. You only need 30 minutes of a short rest to get ki points back, so this depends greatly on your DM's style (IE how many fights per rests). There are plenty of posts talking about ways to make four elements disciplines cost less, which might be good to review with your DM. As you get higher level the ki points should be less of an issue.