Hi eastcoast2uk,
From the sounds of it, you've decided that you want to live in London and have the commute out to Bracknell 2-3 times a week. This is fine of course, and Bracknell on South West trains route goes back to Waterloo as the big train station in London, so if you were to live around there, you know you'd have less underground and bus etc changes to do. If you choose an area or location close to some of the stops along the route of the train, they'd also be potentially suitable and as a general rule of thumb, the properties you'd rent would be larger - eg 2 bed flat instead of 1 bed in and around central London.
You are right about so many areas as London, greater London and the surrounding home counties of the South East of England are very densely populated and places are very close together. I think you'll need to look at maps, read up more opinions here on UKY, read independant reviews and look at property websites to filter the amount you'd like to spend and evaluate all options and make a shortlist based on your requirements.
I'd personally suggest living a little further out so that you have a quick ride into Central London whenever you feel like it, and the commute to Bracknell is shorter as well. The major positive being that most likely, your £1200 budget for rent will get you a nicer place to live in.
Cheers, DtM! West London & Slough UK!