If you need to do anything international or involving foreign currency, you really need a major full service commercial bank. Credit unions (which have other advantages), S&Ls, etc. typically don't handle foreign transactions on their own, although they might be able to do this through some other full service commercial bank with which they have a relationship.

You probably won't get miles for such checking accounts alone in full service commercial banks, although you might be able to earn miles or points for credit or debit cards from the same bank that are attached to your checking account to a greater or lesser extent.

Some people have liked the USBank PerkCard (Visa) [formerly WorldPerks for Northwest Airlines] for its points that are good for tickets on any airline, but it has always had a nontrivial annual fee (around $100). US Bank focuses on the midwest (where it the OP located? it would help to know this in answering the question) but is a major commercial full service bank, IIRC towward the bottom of the top ten in size.