So you are confused about all of the scooters out there? Well, there is plenty to be confused about.  At last count, I had bought 8 scooters and mopeds, six of them on eBay and I can tell you at least what I have learned.

1) KNOW THE SCOOTER YOU ARE BUYING.  Even though there are dozens of different scooters and many of them sold under different names, you can spend a little time and  learn what is what.  Several scooters look very similar in photos, but perform differently when you are on the road.  Try to get as much information as you can from people who have bought the exact bike you are looking at. If the seller offers several models, ask him or her to explain the differences among them.  Learn about the transmission, for example, and the advantages of two and four stroke engines. TAKE YOUR TIME and do your research. Always.
2) RIDE A FEW SCOOTERS BEFORE BUYING.  The first one you  get on will seem like it is flying, but anyone who lives in a city or town with a scooter population has seen some poor person desperately leaning forward as their scooter strains to hit 25mph.  It is extremely useful to know what to expect before you pull your wallet out.
3) BE SURE TO CONSIDER SHIPPING. When an individual sells a scooter, he or she may not have access to  inexpensive means of shipping and crating, so  the price of your bike may be far higher than otherwise expected.  Many new scooters come in special crates. Maybe your private party seller can get a crate from his local motorcycle or scooter shop.  Maybe you can encourage him or her to learn about the various freight companies. You will want to learn where the nearest terminal is and make arrangements to pick up there. This will save you around $50. Consider local pick up, if you live reasonably close. Most scooters will easily fit into a pickup truck and this gives you a chance for a little bit of face-to-face with your seller.  Just remember: By the time you go to pick it up, you have already promised to pay for it, not to "come and have a look." Honor your commitments.
4) INVESTIGATE YOUR LOCAL LICENSING LAWS so that you won't have to study up before your court date.
5) HAVE A BACKUP PLAN in case your scooter doesn't always run perfectly. Do you have a resource for repair advice and parts?  Most scooters are remarkably reliable, but we live in an age where fewer and fewer people know the principles of simple motor mechanics.  It might be useful to buck that trend.  Little things will go wrong.  But, just as you don't throw shoes away because a lace breaks, you don't have to stop riding your scooter because a $20 part goes bad. Not if you pay attention, at least. 
6) DON'T LET PREJUDICE COST YOU MONEY. But don't ignore obvious signs. Despite what will be hinted to you, a bike with a no-name is probably not made in the factory where they make the famous ones.  That doesn't mean it is no good, but it will explain why you can get it for half as much. Think about the advantages of buying a slightly used bike, but be sure to consider warranty issues.  Decide for yourself whether you want a bike made by a long-established company with a network of dealers or you would prefer to assume that the lookalike will last as long as you want it to. If you go for option B, remember two things: the old saying about "assume" and the equally wise one that holds that Luck is the Residue of Design.  If you maintain it and understand it, almost any modern scooter will give you years of reliable use. If you neglect it and fail to know how or why it works, you can expect trouble.
7) KNOW THE SELLER'S TRACK RECORD. An individual has to overcome a lot here, but most of the good people on eBay ware willing to go the extra mile. A dealer should be able to give you some references, or you can find them in his feedback file.  Be especially careful about people you can't raise on the telephone.  Don't be the first person you know to import a vehicle from another country.
8) WEAR A HELMET because even 20 mph is faster than you want your head to hit the pavement unprotected.