>I'm looking for a reliable place to find a programmer
Have you tried posting in the Commercial Exchange here on WW? Or looked at elance or rentacoder?
>some tips on how we pay someone we only have contact with on the net
20-50% upfront, rest on completion normally works fine.
>and how to ensure the person we choose will be around to fine-tune things in the future
There is no guarantee that they will be around for future work, although if you treat and pay them well then normally they will be very helpful in the future.
>how much we should pay
A price you are both happy with, rates depend on skills, job etc.
I find that finding good freelancers online is a matter of trial and error, you find some good and some bad, once you find a good one try and keep them happy for lots of further work.