As someone who's experienced laser hair removal:
It's quite expensive - you're probably looking at roughly £600 for 8 laser treatments each lasting maybe 30-60mins. Unless you're naturally not particularly hairy down there, it'll take more than that - I got recommended to have 12. I've currently had 8 & do need more. (although as you're female you'll probably have a natural advantage over guys in this area) . After you've had your full set of treatments then you're meant to go back occasionally for top-ups (annually if I remember correctly) .
Laser hair removal is quite dependent on hair colour & skin pigmentation - light skin & dark hair will have the best results. You also have to avoid getting a tan which , unless you like nudist sunbathing, probably isn't an issue around your pubic areas but could be around your arms/pits.
Pain - there's definitely some pain involved but 95% of the time it's quite bearable. Occasionally one blast of the laser will have you wanting to cry out. I've never experienced waxing so I can't describe if they're similar but I have heard that can be painful too.
What I would say is that getting tapped but one of those electric flyswatter tennis-racket type things is more painful . Basically, expect some pain but don't let it put you off.
I personally found the worst part of the treatment was actually after the laser had finished as you then have to hold an ice pack to the area to cool it - it's bloody uncomfortable lol.
I know the company I went with gave out a free test session to ensure compatibility so I definitely recommend you try that before spending your money.