Yes, you can get a good quality car for $3000-$4000, e.g., low miles, some exterior scratches, but runs well.
Older cars are not quite as reliable, but as you take TTC to earn your money, the once or twice a year that you take it in for routine service or a weird noise / light / etc... (e.g., not on your personal schedule) will not matter.
Also, if you park outside all winter, that is a bit harder on old cars, too, so be warned to have good battery / tires.