I think most of us use a combination. Personally, I have a couple cases of 12oz bottles I bought from the HBS. I have a couple dozen 22oz bombers, some that I bought new, most of which I saved from some of the local microbrews. I have some bottles I have cleaned and de-labeled - NO SCREW TOPS. Tougher to get a good seal with screw-tops, you could use them in a pinch but it's usually not a good idea. They are also usually a thinner glass, i.e. much more prone to breakage. I make sure not to buy beers with screw tops, the bottle ends up being a waste.
My wife bought me a case of the swing-top bottles when she bought me my kit. I've bought some sparkling french lemonade that comes in a bigger swing-top bottle.
So, it's a definate mix. Tend to think that's pretty common around here.
Things to keep in mind - if you use clear bottles (or green, or blue), you have to be very careful about light. If your beer is exposed to sunlight or fluerescent light for an extended period, it'll get skunky. Simple solution, keep it in boxes, in the basement, in the closet, out of the light. This is less of an issue for brown or amber bottles, although I personally try to keep them in the dark as well.
If you use the swing-top bottles, make sure you take off and sanitize the rings before each use (and replace them periodically).
It's a lot easier to wash your bottles out as you go rather than letting them pile up and the crud to dry out inside. Little soap and hot water, a quick rinse, and they'll just need to be sanitized on bottling day.
Lots of ideas and approaches to de-labeling bottles - ammonia, oxy-clean, and others.
As you get more involved in the process, you may want to consider kegging - but nothing to worry about immediately.