need some advice on bsx bike sizes

I am a 28 year old American recently emigrated to North Wales. I don't have a UK driving license yet
and to get to my place of employment is just a short ride away. It is only about a 15-20 minute ride
on my wifes comfort 4 speed, but I am definitely going to get a decent bike for myself as I don't
anticipate getting a car for another 4 years if I can help it.

The type of bike I am looking for seems to be more in the jump/street range. Something like a
24" with no front mech and a 7-9 speed rear mech. I am looking to build my own. The question I
have is this: I stand 5'10", so what size frame should I go for?

And if there is anyone out there who knows of a good shop in North Wales, don't hesitate to
let me know.