I view private sales (and selling privately) as an EPIC waste of time. If finances allow, buy the car from a 'reputable' dealership/group. This gives you buyer protection, warranty and many other things that a private deals do not with the beauty that it takes less time.
If you know what you are looking for you will generally find a much better deal from a private buyer. There is also usually a better scope for negotiation and a much bigger selection of cars. dealers are just as likely to sell a poor car if they wan't rid and palm you off with some 3rd party useless warranty..