I think that which type of engine you buy is pretty personal. For me I won't buy a 2 stroke because I believe them to be polluters, so a 4 stroke is for me. Also there are a lot of options for where you mount your engine- in the frame or rack mount.
Also everyone has their personal feelings on each of these.
for
2 stroke info go here
for 4 stroke here
frame mount
rack mount
As for who to buy from, there are a lot of vendors. You can check ebay, stay away from revolution Cycles though. I made the choice to buy an engine and work my way out from there. I'm buying the parts as I have time and money. I got my bike and engine off craigslist but I'll be buying my sprockets from Livefastmotors.com
I like livefastmotors because they have items specifically designed for the schwinn stingray, but that's me. Again to each their own.
I have to agree with bluegoatwoods that the search feature is a little winky on here.
try these search terms
HT 80cc speed
HT is short for Happy Time- that's what a lot of people call the little 2 strokers another thing they call them is chengine try searching that term as well see what you get! I was pretty confused about the different terminology when I first started surfing this site!