Professional waxing will usually yield 2-3 weeks of hair free bliss, and another 2-4 weeks of smallish hair growth. By the end of 1.5 months or so, you'll be ready for a second application.
Different people, different areas of the body, etc will provide much variation in time frames.
Laser on the upper lip is painful (and permanent), but also should be less expensive than doing the entire beard/neck area (which in my neighborhood costs about $100/session; 6 sessions are recommended and often there are package deals or seasonal deals, "buy1/get 2" etc)