Things to think about:
- Almost every class has a big power spike at 5th level; 3rd-level spells for casters, Extra Attack for martial types. If you start multiclassing before level 5, you risk falling way behind your single-classed companions till you hit 5th in something. Consider how you can stack class abilities to compensate. As Kerleth points out, Hex + Flurry is a good monklock combo to let you make up the damage you lose by not getting Extra Attack right away.
- If possible, it's good to stack your class levels in increments of 4 so you don't miss out on feats/ability boosts. Those are a big deal. However, it won't kill you to wait an extra level or two before getting your levels sorted into nice 4-blocks.
- We recently got a ruling that warlock invocations use warlock level for prereqs, not character level. This killed a lot of XXX/lock builds.
- Consider carefully what you want out of your character. I played a cleric 4/wizard 8 for a while; he was perfectly effective in his role, but in the end he was unsatisfying compared to a 12th-level single-classed wizard. I found that I wanted access to the high-level wizard spells and advanced class abilities more than I wanted access to a smattering of clerical magic and armor. If there are particular monk abilities you really look forward to, consider going for them first and multiclassing later.