At that range, expect 30% tax; rent is about 8k-10k/m. That and transport could total to half of your non-tax budget.

With an income of 37,500 SEK/month (salaries in Sweden are generally discussed as a monthly number, not yearly) in Stockholm, you're going to be paying around 25% in income tax (according to http://www.ekonomifakta.se/Fakta/Skatter/Rakna-pa-dina-skatt... which is a calculator).

Average rent is very very hard to answer, it will depend on a bunch of factors such as location, building age, the exact form of contract, and so on. Getting a "pure" rental apartment is very very difficult, the required queue times to get one in central Stockholm are silly.

This list http://www.hemhyra.se/stockholm/stockholms-dyraste-och-billi... (in Swedish, but it's mostly street names and prices) show values between 320 and 1,745 SEK/m^2/year. Homes in Sweden are always specified using the exact floor area in square meters.