I just went through the same process when I bought my "new to me" Cadillac STS a few weeks ago. (
Pictures and Info here. ) I looked at private party cars, but ended up buying from a Cadillac dealer.
One big advantage a dealer can offer, that I recommend you strongly consider, is the "Certified Pre-Owned", or "CPO" program. This program is only offered by the franchised new car dealers on their used cars of the same make. (i.e. a Cadillac dealer is the only one that can offer a "Certified Pre-Owned" Cadillac). A CPO car will cost more, but they have been through an extensive inspection (which the dealer should provide you with the report and the repair order for any corrective work done). My car had brand new tires and brake pads installed as part of CPO. The best part is that the FULL, NO DEDUCTIBLE bumper-to-bumper warranty is in effect until 6 years, 100,000 miles from original in-service date! And this warranty is backed by GM, not some fly-by-nite warranty company (several have gone belly up, leaving warranty holders with worthless paper). How's that for no worries of being nickel and dimed!! With how complex these cars are, that's just huge peace of mind for me. Again, it does cost more (the salesman told me that Cadillac charges the dealer about $1,500 to CPO a car). But for me it was well worth it.
Additionally, a GM dealer should be willing to go into their GM online system and print you out the full history of the car you are considering. You can get the build sheet, and you can see if it was orginally a fleet or rental car (vs. private individual or a leasing co.) and what sort of warranty repairs were performed. I learned that my car was purchased brand new at retail, by a couple in their 60's who then traded it in on a newer Cadillac with only 34,000 miles on it. It sincerely looks BRAND NEW and I can see that the warranty work done on it has been only a few very minor glitches since new. Again, peace of mind.
Speak to the former owners of the car if you can, and if you can get (or see) their maintenance / oil change records, all the better. The prior owners of my car were happy to talk by phone and gave me a lot of comfort that the car truly was well cared for.
There are a fair number of low mileage cream puffs out there. If you are not in a big hurry, you'll find a nice car eventually. If you develop a relationship with a good salesman at a dealership he can steer you to a nice trade-in before it goes on the lot. Again, buying CPO from a dealer will cost a bit more, but will bring very significant risk reduction in your car.
Good luck, enjoy the hunt, and most importantly, enjoy your car when you find it!!