As far as rents go, if you get your own 1 bed studio, with bills you're looking at $1k a month after bills. If you share with other people as 99% of students do, you'll spend about $500 a month. This is pretty reasonable really, that's cheaper than I pay in the UK.
Public transport is good, buses cover all the important areas of the city, downtown, the mall, the uni, and the nearby towns. Tickets are $2.25 a single no matter how long the journey. They are frequent too.
Weather, well this is the so so side of living here. On the one hand, St. John's is the foggiest, cloudiest, wettest and windiest city in Canada (not all at once, but chances are at least one of these will be present at all times). The upside is winter temps are milder than most areas of Canada, it's actually has the warmest (well least cold) climate outside of British Columbia.
Hope this hasn't put you off, it's a truly lovely city, although it is as I said an outpost. A booming outpost with a good variety of shops, a lot of part time job opportunities and 100,000 very friendly people. But the nearest big city is Halifax, a good 1000 miles away so make a lot of friends and enjoy either being in the comfort of St. John's, or travelling through the wilderness of Newfoundland (which is great fun) to keep you occupied.