Tampa is pretty big but not used buy internationals a lot.
I think BA arrive in the 'E zone' (Check as it might have changed). On arrival there is a long walk to Immigration. It should be a small wait as few others. When you come out note if you are in 'Blue1 or 2' or 'Red 1 or 2'. That is the 4 corners of the airport. When you leave go back the same way. (If not don't worry as all meet up, just walk further)
All major car hire co.s there, plus a pick up and dail free phone to nearby hotels in baggage claim. Car co.s have shuttle busses, if you call them they will ask where you are waiting Blue 1/2 etc.
Airport is on 3 levels - Departures / Arrivals / Cars / Taxi's etc. (I think) Watch the escalators, some go 1 level other 2 levels. But it is easy
Depart. reversal of above really. BA departs from a gate at the very end of the pier so it is a bit of a walk. Any duty free purchases are handed to you as you board, not collected when you pay. BA's flights have BA staff there so very good, queue's can get long but the process quickly, opens about 4hrs before departure.
Very spacious airport. About 12 / 15 shops, nothing great but covers everything. Great hotel if you want a good meal before going, if not several other eating places, TGIF, McD's, Seafood.
Airport is just off I4 so easy to get to Orlando (1 1/2 - 2 hours) plus Brandon mall close by and Busch Gardens.
Please PM me for further details
C