Yes, you'll need a winter coat when it's winter. However, you can buy one once you get here. In late August/early September, it'll be in the high 90s. It's not always winter.
2 bedroom apartments are between $500-$700, depending on the area. If you don't care about living close to campus, look for apartments in South Fargo. The commute is 15-30 minutes, but the apartments are much newer. I live in an old triplex near campus and it's crappy/cheap. It depends on the quality of apartment that you are looking for. The apartments around campus are older except for T-Lofts (http://www.roers.com/t-loft-apartments/home), a new complex South of campus. It's overpriced though. I know many grad students who live in T-Lofts their first year (for convenience) and then move to other parts of the city. There are also apartment buildings further south of campus (on College Street) that are newer. Also, there are newly built, 3 story town homes within walking distance of campus for $1100/month.
For on-campus apartments, the Niskanen apartments are newer and located in the University Village area NE of campus. There is a bus that continually takes students from University Village to campus. The apartments that are labeled "University Village" are older/cheaper and in the same area. However, mainly international students seem to live in those.
Downtown Fargo has been revitalized within the last 10 years. There are unique restaurants and shops. Also, there is a rather large bar scene downtown. We have at least 3 small breweries in Fargo/Moorhead. The art community is growing too. It's a nice place to live, except for the terrible temperatures in the winter and the humidity in the summer. However, every place has something that sucks about it.
On the plus side, NDSU also has a great football team (4 consecutive D1 national championships) and is an R1 university.