Hey, I've been pretty much looking for a car in the same price range and the same area for the last few weeks (not looking too seriously until I get cleared on a loan though...woe is me, and there's a lot to be had if you're vigilant.
I was in pretty much the exact same boat this time last year and ended up with an 89 tercel with about 90,000 km on it. It ran great (but yeah, the feedback carb could have been a problem in colder weather or in a few years) until I wrote it off.
Civics and tercels depreciate very slowly in Vancouver, so they're a good investment, but a bit of a pain to find for a steal. With $6000 you could probably get a good civic around a 93-94 model year or earlier, but it'll probably have a lot of mileage on it. A tercel won't have as much oomph (they're not quite as powerfull as a corolla), but you could probably get something newer and with less mileage for the same ammount of money, and the insurance won't be quite as steep. In my opinion, they aren't up their with civics as far as performance is concerned (and hills may be a bit of a problem, but I never had a problem getting it up to 95 or so on the upperlevels cut in north vancouver - highway 1, if you know where that is).
Honestly, I'd stay away from anything domestic with the ammount of money you're willing to spend. You could probably get something newer and that looks nicer, like a 99 or 2000 cavalier, but there's a good reason for that- they aren't as reliable.
The tercel switched to the 3ee fuel injected engine in 90 or 91 I believe, but later models (from '92 or 93 on I think) are all coup or sedan, so if you wanted a hatchback you're going to be looking at an early 90's tercel, a civic (any year) or a Hyundai Accent (not sure which years offer hatchbacks, but they have a unique styling...if that matters).
I'm not too sure what to think of the accents. The price is very good and tempting, and many reviews have reccomended them as used cars (97 and newer I believe), but there's also mixed reviews. I don't believe they're quite as reliable as the civics or tercels, but then again, we're talking older models of civic or tercel in the same price point, so it could be a toss up pretty much.
Also, I'd actually keep an open mind and consider getting a manual transmision. This will give you a lot more freedom when looking for a car, could save you a few hundred bucks in the sale, and it's probably something that's good to know anyways (I've never really driven standard either, but I think I'm going to get a standard car this time around).
And when dealing with dealerships, two sites you may want to check out are:
1.) The Motor Dealer Council of BC(
http://www.mdcbc.com/} and
2.) The BBB of BC (find a company report page:
http://www.bbbvan.org/company_reports/find_report/index.cfm).
Good Luck, and an infinite resource of information can be found in your library. Look for the Lemon-aid books by Phil Emerson (if I spelled that right). A ton of information about buying a used car in canada can be found in those.
