Make sure if you do go private that the le is in their actual name because the le offices are getting very strict about transfers. Also go and pick up an "Application for Certificate of le" form because the seller will have to sign that too. If the seller owes a balance on the vehicle don't pay the seller. Go in person or call the bank that has the note and pay them direct because they're the ones with the le.
One thing to consider about private sales is that you will have to pay tax on the value of the vehicle not the sale price. So if you find a 20k car for 14k you have to pay tax on the 20k value not the 14k purchase price. This is to avoid the old "birthday or gift" tax scam.
At a dealer you only pay tax on your purchase price so if you get a great deal you won't get the tax shaft.