I live in Karachi so absolutely no idea. Why don't you call the helplines of different banks and ask if they provide in BWP?. You can get a fair amount of idea on their websites as well. Some of them offer online forms as well.
However, I would prefer to go to the branch itself and inquire. Things like hidden terms, upfront costs, transaction limits, Internet banking, especially "payment procedures" become clear only when you inquire manager, etc in the office. Even in Karachi, some branches don't support CC payments and/or have drop boxes so you have to move to another branch, etc.
In general, banks are a pain the a**, so it's better to have one nearby where you can vent your anger upon if something goes wrong (like your nearest is in LHR). Try to get from any bank which is nearEST.
Since you have a job, with a salary slip, you should get a credit card. However, BE WARNED - credit card (al tough they bring in more PREMIUM services than a debit card) is a postpaid thing.. any misuse on it can be even more dangerous than a prepaid one.. (at least in UBL.. you cant have sessions on their credit card, anyone having you card and CVV can misuse it). You get higher rates when you miss payment by even 1 hour, etc, etc, etc (it's a more good recipe of bank profit). If you can live without it, try to avoid it.
PS: Do Google as well! I remember only Bank Alfalah, Standard Chartered (from this forum)..