If I fly through London Heathrow, arriving on American, and on to Prague on British Air and it is booked all together.
Will I have to retrieve my bags and go through customs in London?
If so, what is the minimum recommended time to allow for this layover?
One of the possible flight options just gives me an hour in London, while another gives 5 hours.
I would have no confidence in a layover of only an hour at Heathrow. To begin with, you're almost certainly going to need to change terminals. Long-haul AA flights arrive in Terminal 3 (https://www.heathrow-airport-guide.co.uk). All BA flights operate out of Terminal 5. To get from Terminal 3 to 5, you need to take the Heathrow Express train service. This service runs every 15 minutes, and estimated travel time is 20 minutes (http://www.heathrow.com/airport-guide/getting-around-heathrow/travel-between-terminals). This means you're looking at a possible 35 minutes in travel time alone.
Once you're at Terminal 5, you're still not guaranteed a simple dash to your gate. Terminal 5 consists of three concourses: A, B and C. Only the A gates are located in the main building. If your flight leaves from the B or C concourses, you need to take an additional shuttle train. From there, the actual walk to your gate may take up to an additional 10 minutes.
As a final complication, many BA flights require the use of shuttle buses to get from the gate to the plane. Because of this, BA guidelines indicate you must be at your departure gate at least 20 minutes before your flight departs.
In my opinion, leaving yourself an hour layover an Heathrow is nowhere near enough. I would not be comfortable with anything less than two hours.
Choose what company recommend you. Usually you should not collect the baggage, but check-in/baggage-drop will confirm you where you should collect the baggage..
Don't worry about missing the flight. You will be rebooked to the next flight.
Since it's in a single booking, feel free to take the shortest connection, because if you miss it, the airline is obliged to put you on the next flight for free.
You also don't need to collect luggage.
I don't think an hour is enough. I had to do this connection. My first flight left late and I had only 25 minutes left. I missed my connection and was stuck in London for a day. The truth is the airline was only willing to put me on a flight three days away but I shelled out an extra $1100 and got out of Heathrow on the very next flight 24 hours later.
