Generally speaking, if you're South of the river (and to a lesser extent, East of the railway station) you will be close to a bus stop. A lot of bus stops in the city centre will have buses going to the university every ten minutes or so. I'd recommend looking in places like Hala, Scotforth, Moorgate, Bowerham and Greaves. I lived in Moorgate for three years so I can vouch that it's a fairly decent place: close enough to the city centre that you can nip in on a whim but far enough away that it's relatively quiet at night and cheap(ish). Scotforth is about half way between the university and the town, realistically you'd get a bus whenever you wanted to go to either if you were living there.
I would avoid the Ridge estate though, there are buses between it and the city centre then but you're no longer looking at direct buses to the campus. It's also one of the less desirable parts of Lancaster. West of the railway station and North of the river have similar problems. There are buses that run directly to the university from Morecambe/Heysham however there are fewer routes that go this way so the buses are less frequent and they'll take quite a while. From the centre of the city it takes about 10-20 minutes to get to the university depending on the route and the traffic.
As for accommodation providers, a lot of people go with LUSU Living as they're affiliated with the students union. In my opinion (and many others I've spoken to) they are pretty incompetent and treat their clients as cash cows rather than human beings. Other possibilities you may want to look at are Yellow Door Lets and Student Housing Lancaster. Yellow Doors are generally decent from what I've heard but all of the front doors of their properties are painted bright yellow which is a huge magnet for burglars as it means there is unlikely to be anyone staying there during university holidays. I've heard their service is reasonably good though and they send out people to do repairs efficiently. Also I think you can get half price rent during the summer.
I would not recommend going with a private landlord unless you really want to and they have good reviews online as there are a few who are known to be crooks who refuse to do repairs/don't put the deposit in the place they're legally obligated to/have houses of substandard quality etc. Unfortunately I can't remember any of their names right now.