It looks like this flight is frequently an A380 which is a two deck plane, but there’s no guarantee that the aircraft type doesn’t change at some point. The upper deck is a mix of business, premium economy and economy. First class is downstairs. There’s a seat map here https://www.aerolopa.com/ba-type-38a

Unless you have status with BA you have to pay to chose your seats, unless waiting until 24 hours before flight time.

Edit: I was way too slow.