My 2 cents having bought my fair share of vehicles over the years:
Buying used you will be purchasing wither from a private seller, used car dealer (Joe's Auto Sales, etc), or a dealer (Toyota, etc) from their selection of trade ins. I personally would steer clear of the used car dealers. Not to say that everything they have is junk; however, IMO a lot of them are "shifty."
That being said, private sellers can be shifty too, and in some cases will lie right to your face. Even the dealership may have "accidentally missed" something on their inspection report after the vehicle was traded in.
Bottom line: whatever you are thinking of buying from wherever/whoever, I would strongly suggest taking it to a mechanic ELSEWHERE, preferably a mechanic who you know and trust. Someone who will give the vehicle more than a quick once over. A used vehicle in the 13-16K range with 90,000ish km on it almost certainly needs SOME work. Unless the previous owner stayed on top of every little thing before they sold it. This is unlikely as most people don't sink money into a vehicle they are getting close to getting rid of.
You want to buy a "cherry" used vehicle. The pick of the litter. Something treated well and maintained. Not something that you will have to sink bags of money into, worst case scenario a lemon that the previous owner got rid of.
A few other thoughts:
-Private sale? Hopefully the owner kept maintenance/parts receipts. If yes I would want to look them over. Dealers typically shred these receipts for privacy reasons BUT, if you go to the service counter at the dealer that sells the vehicle (for instance, you are looking at a used Toyota, you can go to any Toyota dealer for this) and give them the VIN #, they can run it. When they do this on their screen will pop up all maintenance that was done on the vehicle at any Toyota dealer, any warranty work, any recalls, and so on. Basically any time the vehicle was in at the dealer for ANYTHING, they will have a record of it. They will not print this record off for you, but they should have no problem showing you the computer screen.
-If the seller has the Carfax/Carproof report for the vehicle, great, give it a good look over for how many ppl have owned the vehicle, accidents, and so on. If it's a private sale and the seller does not have this report I would pay yourself to acquire it.
-Before you pull the pin do a google search on the particular vehicle and read some consumer reports and so on. Make sure this was not a bad year, bad motor, recalls, and so on.
Bottom line, if you put in the effort you can find a great used vehicle in your price range. Your time and a couple hundred bucks for the inspection will be well worth it in the long run. I personally have an affinity for Toyoyas, but I would say buy whatever you want/like, just make sure you are not buying someone else's problem.