Mattd
This has been asked and answered many, many times before!
However,
It greatly depends upon what fleet and therefore what base you have. The 737 is the only Gatwick based fleet and tends to run more day trips and uses a rostering system called Carmen. It does benefit junior pilots as you bid for your days off and the system attempts to fill your 'work' days with work and keep your 'off' days 'off'. For a joiner it is, potentially, better than being junior on Bidline. Normal Short Haul blocks of work vary around six day blocks. I have never experienced Carmen so I cannot say how it would fit communting. I do know that most of the 737 junior FO's live near the airport.
The Airbus is based at Heathrow therefore comes under the Bidline system where you bid for your work based upon lines of work and preferred days off. The most senior can 'custom build' a line of work to suit them at stage 2 bidding but most pilots will choose a built line at stage one and then 'fill' at stage two. As you can guess this is a system that takes getting used to! Most importantly it is a seniority based system. Therefore if two pilots bid for the same line then the most senior gets it.
Where does this put you as a commuter? The company builds 'commuter lines' built with long, high credit, 5 day trips and four day trips meaning you can do those and have 4/5 days off in between. The only danger with being junior is that you probably won't get them as have to live with 'blind lines' where the company fills you line with work no one else wants.
Many do commute, there is a very healthy line of B&B bedrooms and flats on the company notice board and most flight crew will give up jump seats for you.
As with anything BA it can be a little tough at the start but if you get in now and then the rest follow you will find that you aren't at the bottom for very long.
Good luck