Kinda ironic that you bring this up today as I am preparing the documentation to submit my car to BaT...
I have purchased two cars from the site over the years and that went smoothly both times.
As far as selling, the costs range anywhere from $100 on up, depending on what type of ad and whether you want to splash for professional pictures and detailing or not. Simply go to their home page and click on the 'submit a vehicle' tab and read - its fairly straightforward. I have not sold anything there yet, but a friendly acquaintance has peddled several vehicles there over the years and says its really quite simple. HOWEVER - as has been noted - one must 'submit' the vehicle for 'approval'. These days - since the site was sold to a major media conglomerate [hearst I believe but don't quote me] it has become basically an online high end used car lot; seems only one out of every 4 or 5 cars is something other than a late model Porsche or BMW and is not being sold by a dealer. They do however have some interesting/affordable cars and bikes, you just hafta get lucky and hope your submission tickles the 'screener's ' fancy. The 300 is unique enough that I would imagine it will be accepted. And BaT seems to like old wagons these days.
BaT has a huge following across the country and even the world. Cars seem to bring silly money on that site - best of luck. And wish me the same...