When I helped my mother sell her car, we did a couple things that helped:
-We printed the Carfax report. I know we regulars in this forum know a Carfax reports can be completely useless, but it does make many buyers feel better.
-We printed a complete report from the Kelley Blue Book website on her car, which showed it was worth what we were asking.
-We stuck a sign in the window so people would see the proverbial "little old lady" driving it around. If you aren't a little old lady, stick a sign in the window and loan the car to your mother or aunt to create the "little old lady" facade.
In spite of spending money to advertise the car online and in the newspaper, my mother ended up selling it to someone who saw the sign in the window. The buyer didn't even haggle, she just paid the asking price.
I don't recommend buying new tires for a car you're about to sell. Nobody is going to pay more for a car just because it has new tires, and you won't recuperate what you spend on a new set of tires. If your tires are completely worn out, shame on you for driving on bald tires. That's dangerous. If you have to replace the tires in order to make it safe for a test drive, consider used tires, but only if you can get a matching set. Having four different tires on your car is a bad sign.