A.R.
We have sold several cars privately. I never deal with the people or meet anyone alone. Typically my husband and I meet the prospective buyer at a public location. A mall is a great idea because a test drive can consistent of my husband riding shotgun or in the backseat while the prospective buyer gives the car a spin. We both make it known we have cell phones on us (usually we both have them in hand) and we also mention we are expected at dinner at mom's in a short while. The dinner ploy also gives the prospective buyer time to think if necessary. They know upfront you aren't in a rush to sell since you have other plans and can wait on them to think.
We never involve a mechanic unless the prospective buyer brings one. So far no one has gone that route.
Definitely know your values. KBB as Jim mentioned is a good source. BUT despite what KBB thinks your car is worth, the market/demand will really drive the interest and hence the price. We have had two cream puff cars which wouldn't freaking sell because no one was interested in them. That sucked big time and we took a hit on both cars.
If you aren't getting a lot of interest in your vehicle postings, take a look at your competition and their prices. You may be priced a little high OR your vehicle might be in worse condition/uglier color/fewer options/etc OR you may be falling outside of a price search bracket. In other words if someone does a search for 2k - 5k and yours is 5.5k, then your vehicle listing won't come up. I trust that part makes sense.
If cash is being used to purchase the vehicle, then we meet in the lobby of a bank. Any public location would do but banks seems sensible because they are used to seeing folks with large amounts of cash. Also there is a security person available. Otherwise, we ask for a cashier's check and exchange that in a public place.
We always print and bring two copies of a bill of sale. We have the forms filled out with the necessary information beforehand (VIN, mileage, make, model, color, etc.) and we have both copies signed. We keep one original and the buyer keeps the other. It's a good idea to have the contact information of the buyer (phone number and address). Once we had a ticket mailed to us beacuse the buyer didn't transfer the title. It was a good thing we had his phone number because he had wracked up a ton of tickets. Our state also allows you to mail in a form to the state indicating you no longer own a vehicle. That provides you protection when someone does what that guy did. See if your state has a similar program.
I don't know how your state works but we also take the vehicle title transfer paperwork. The buyer keeps that for transferring the title into his or her name. Our state DMV website also has other helpful tips about buying/selling a used vehicle. Good luck. It's not that bad and most people are honest and normal.