OBD and OBD II are systems for turning on the "CHECK ENGINE" type lights but where they really do their work is in putting a code into a vehicle's computer memory. If a problem goes away in say 50 start cycles, the code clears. If the problem is something that is sticking around, then a code remains as well.
Getting a shop that checks for these codes to do your inspection is critical and if you need to see a "smoking gun" for problems, the diagnostic code readout will provide it.
My mechanic uses an unit that is around the size of a mousepad. It may be a good idea to buy one for one's own use since it will be used to buy the vehicle you want as well as find problem areas out in the time of your owning the vehicle. If you find the problem is a simple one like replacing the O2 sensor, then the labor savings will be able to pay off the device's cost in time.
After buying a vehicle I would also recommend buying the shop manual for the vehicle. It's the same manual that the dealerships use. They are thick, heavy and loaded with tons of good info. I've bought them on
eBay for prices ranging from $30 to $60, which is less than one hour's cost of shop time these days. Even though I do not do my own work any more, my mechs and techs appreciate having the manual to show them the tricks of my car, which saves them time and me money. If you do work on your own vehicle, the shop manual will pay for itself many times over.
Transmissions are easy to figure out if they are going bad. Pull out the dipstick, then see and smell the fluid. It should be red and have little smell when the ****** is good. Brown and a burnt smell show the ****** is on it's last legs. Even when you get a good ******, you protect it by adding an outboard ****** cooler. Back in the Good Old Days of big engines, big radiators and big transmissions, the failure rate was not that high but today with hotter engines and everything being made smaller, the design parameters are squeezed right to the edge, so the ****** becomes rather vulmerable in today's vehicles other than the big trucks like F-250's/350's, which are set up for Big Boy hauling jobs.
I could write a small book on how to buy a vehicle but it would bore the hell out of the "don't like long posts" crowd...LOL! The short and sweet of it is that most problems are amazingly obvious to spot if you know where to look and what to look for. The other thing I'll add in is that no matter how good you are at buying vehicles, 10% of all vehicles go bad in the end based on my life experience. Must be a Murphy's Law corollary!
Rick