I would definitely suggest doing some more research. The "vent" you are referring to is called the chimney (or stove pipe) and it is absolutely 100% necessary. It is how all the smoke, CO, etc. safely exits your home. There are ventless gas stoves, but even these are not that great of an idea, IMO.
You will need to check local codes but there are typically minimum specs for distance of the stove to combustibles, double-wall vs. single wall chimney pipe, heat shields, area of hearth in front of and underneath the stove and height of the chimney top from the roof line. It isn't just slapping something together and building a fire if you are doing it correctly.
Also keep in mind that your insurance rate may increase. A home with a woodstove was more expensive to insure than a home without due to the increased risk of fire when I lived in MI. You could not report that you installed one but if you have a fire and they figure out there was a woodstove in the house, good luck filling a claim.
If you are going to get a stove, think about supplemental cooking along with supplemental heating. I'm guessing you want the stove so you can still heat if the power is out and/or there is a petroleum fuel shortage or price increase? A lot of stoves look very nice but don't have an area on top large or flat enough for a pan. Just something to think about.
My parents have always had Jotul brand stoves. They are pricey but very high quality, efficient and you can cook on most. If/when I have a home again, a Jotul will be installed. Here is an owners manual that talks about installation so you can get an idea:
http://www.jotul.com/FileArchive/Te...CB Black Bear/Manual_F_118_USA_P04_050508.pdf