Thanks all for your replies. I just wanted to keep you up-to-date . . .
Slartibartfast -- That was an excellent list that you posted, I really do appreciate it.
I have decided that I'm going to go through a dealership instead of private party. Yes private party is cheaper, and I have called many (through Craigs List and word-of-mouth.) I was very surprised as to how hedgy these people were when I asked specific questions, like "How many miles are on the tires?" "How new are the brakes?" "When was the last oil change" "Do you have maintenance records?"
Not one of them were willing to let me take the car to my mechanic for inspection.
All of these cars were either close to or way over 100K miles, but they were in the price range of what I'm receiving for my totaled car.
I called a car dealership that had, what I thought was perfect (web-site viewing) and the owner told me about the car then said "But you really don't want this car." Then he proceeded to talk to me about other cars he had available for more than 10K over what I was looking at. Whenever I tried to steer him back to the car I saw on his web-site . . . he just put me off.
I talked to CarMax, and while they seem reputable and back their cars, they don't have anything for under 10K. However their cars have lower mileage and are newer. I might just bite the bullet and go with paying more.
I have another dealership that I need to call tomorrow. They have 3 cars that are a little bit higher than my price range, but lower than CarMax. I'll get out to look at them on Tuesday . . . keeping my fingers crossed.
Oy! What a hassle. Sigh.
I really appreciate everybody's help and input. I'd be going up a creek without a paddle if it weren't for you.