Ah, Milan via Heathrow... coming from the west coast it is a common option. I've spent way more time in Terminal 5 than I would have liked. Heathrow transfers require a lot of walking and lot of escalators so there's no rush you're in for the long haul when you get off the plane.
Heathrow is busy but 2.5 hours is fine. If BA books it for you it should work but I would start to be nervous under 1.5 hours. Follow the purple signage for foreigners traversing Heathrow onto Europe. You will need to go through security again - many lines usually fast even if the space is crowded - and then into Terminal 5. This is internal 'already in Terminal 5 security' not the same security as the person off the street.
Pret-a-Manger is your friend or Starbucks if you just want coffee most everything else is fancier sit down restaurants, stores or duty free style shops. You are post security so you can get drinks and whatever you want without concerns. The seating will probably be crowded.
The single biggest tip for Terminal 5 is only A gates depart from the main terminal. B and C gates require yet more walking and a tram so if your gate comes up B or C start the transition as soon as you know. Now sometimes they will say "Departs C gates" when you arrive so you can get started early. Food options are limited at outer gates - Starbucks only on at B AFAIR - so if you want to get a sandwich grab one at Pret-a-Manger and then head directly to the B or C gates before eating.
For the airports MXP is further away from the city than LIN but better connected via transportation so MXP is probably the better choice for getting into the center of Milan via train or bus.
Beyond that both Ryan and Easyjet hate luggage with a passion so make sure you've paid enough for your carry-on as a bag when checking pricing. Their "carry-on" sizes are very small.
Have a great trip, post airports anyway,
=Tod
