I am going to study medicine out of my city, but there's no Internet connection, I've been looking at Mobile broadband, but I know that it is kind of expensive, beside being really slow and having a mb limit, I also have look at other options, like satellite Internet, but either they have bad connectivity or they are expensive. Is there any type of Internet connection available.
If there's no wired solution, then mobile or satellite are probably your only options. If you can get good 3G or LTE in the apartment then mobile broadband will probably be perfectly sufficient. I would take a look around for a cheap operator. Here in the UK we have one called GiffGaff who offer unlimited data for £12 a month. You probably won't be able to use it for huge amounts of video streaming, but apart from that it should be perfectly sufficient. Satellite broadband is also surprisingly good. I have a friend who has 18mbps down over satellite, although the data cap is quite low and it's expensive. I guess you could speak to the university or real estate people and see if you can get them to set up some sort of wireless link to the apartments; it's perfectly possible over 1km using standard wifi if you have line of site. That would rely on the connection at the other end having bandwidth to spare, however.
I have look at the broadbands, from my country (Mexico ) actually the monthly cost, is almost equal to what I would pay, for the rent, so is expensive, and is also slow, but I think it would be my only option since satellite Internet is really expensive here and there is not a major distributor.
I'm not sure how far "out of my city" you will be, or how much internet you are looking for. This may no longer be an option, and if it is it may not be an option much longer, but: When I was traveling outside the US to a remote area with no internet access before the smartphone revolution (so likely much more remote than you will be), I bought a (first generation) kindle. There is a rudimentary browser that was in beta-- horrible interface, truly, and incredibly slow-- but perfectly sufficient for checking email and the like. And it was free and unlimited. It sounds like you need "real" internet-- good bandwidth and the like. But if you're looking for cheap and better than nothing, someplace with no options besides satellite, I'll bet you could find one of these used somewhere and have a basic text interface.
o sorry for not specifying. I moving to a new city (town), that only university an a residential area of apartments, but for right now there's no Internet connection in the city except in the university and the real Estate building and both are like 1 km from my house. I have the kinddle 3rd, the free Internet, could be useful on emergency, but I need a better connection to do investigation, and homework.