I've always used craigslist - and had a seperate email account for such - and that email (anonymized) was the only contact info for me available on the CL ad - this lets you easily filter out most of the chaff that comes from CL ads.
State your terms well in the ad: things like "Cash only", "no offers accepted" (or "OBO"), Car is sold as is, where is", "contact me via email only, leave your name, phone number and a best time to call". "If the ad is still up, the car has not been sold"
Also be sure to state things like "willing to sell today", "clear title in hand" (IMPORTANT), "starts and runs" (or "will require a tow truck to move")
I also add a line in the ad that says "please include the words 'I love old rovers" in your response" - this helps weed out people that arent reading closely or are just spam-bots. This might also weed out a few decent responses - but if its a real person replying, their reply will be more than 1 sentence long so you can make your own call there.
Put up your ad, don't be afraid to not respond to people if they dont offer what you are looking for - when is email only, its not like they can (easily) stalk you and bug you until you sell it to them.
Do your best to give the first responders the first chance at the car, but the rule I follow is : the first person here, with cash, that wants the car, gets it. no 'dibs' or favors. Or : "Cash is King". Maybe make exceptions for friends/family (in that case - you offer it to them before putting it on CL)
I dont know anyone who accepts payments from strangers - I'd just blow off those emails - or respond with a polite "contact me when you have my asking price and I'll see what I can do" - then he has your contact info (and you have his b/c you asked for it in the ad) and if he/she magically finds the money - you have a sale.
I have never dealt with ebay - its getting too 'buyer-focused' for me to start selling stuff there now.
And maybe you do all of this stuff already. if so, sorry for telling you what you already know
-John