Notwithstanding the short versus long haul aspect, I would highly recommend that you live close to your base (ideally 20 mins or so). I have lived close to base and also had a 2 hour plus commute to the airport.
The advantage of living close is that your working day will be shorter (hence you will be able to make better use of the rest period between duties), you will not have the stress and expense of a long commute (petrol not getting any cheaper!) and, who knows, you might be able to travel to your report point without needing a car. Very often these days you will have to park at a remote site on the airport and then wait for the perrenial "shuttle bus" to transfer you to the report point. Sod's law says you have just missed the bus when you arrive and have to wait circa 20 mins plus for the next one! This process then has to be repeated on the way back! If you live close you can use a taxi (or maybe public transport) or get your friendly crew member to drop you off at the airport. You also do not have the car rusting away in the crew car park whilst away on duty.
However, in my opinion, the biggest advantage of being close is that you can engage more closely with your employer. You are more inclined to pop in (dare I say it, even on a day off!) to pick up the mail, look at the charts for the next duty (maybe you have never been to Timbucktoo before!) and generally get more involved in the "social" side of the company. Also, when you get back off a trip you don't mind so much taking your time and perhaps picking the brains or swopping stories with fellow crew members. Furthermore if you are close to base you might pick up a good trip at short notice when the company are desparate for a pilot!
Later on in your career, when you "know the ropes" you might decide to live further out (or not) but, to start off with, I would highly recommend living close to base.
Hope this helps!