The chances of both the faucet AND the shutoff being bad are slim, but it does happen, especially if it’s older and even more so with ‘multi-turn’ valves (As opposed to quarter turn/ball valves).
If you have someone replace the valve, get both done and get ball valves put on. Much more reliable.
Having said that, you mentioned that it stops after several minutes. Is it ‘flowing’ or just dripping? You also said this is a condo, I’m going to make the assumption that the shut offs are still below the faucet, right? If (for some odd reason) they’re physically above it, that could a whole different thing, but it’s probably not the case.
Anyways, does it eventually stop? If it does (even if it slows to a drip), you could probably take a crack at replacing the faucet yourself, especially since you said the lines from the shut offs to the faucet are hoses. That means no soldering, not dealing with precut copper pipe and compression fittings. It’s just a matter of having everything ready to go and working fast if it’s dripping. As long as you leave the drain connected and the (new) faucet in the open position while you’re working, if it’s just dribbling or even a small stream, it shouldn’t be too bad. Just empty everything out from under the sink, put down some towels and keep a bucket under it.
Oh, one other thing, I should have asked at the beginning. What happens when you open the faucet all the way and close both of the shut offs? It keeps running a little?
As for a plumber, in a house, shutting off the water, replacing a faucet and two shut offs would probably take an hour plus parts. I’d expect $200-$400. I don’t know if it would be any different in a condo.
One last thing, I noticed you said that when you pulled the knob out slightly it would stop. The valve is probably just wearing out. If the valves under the sink do actually shut the water off, you may be able to buy a kit to rebuild the innards of the faucet at Home Depot. It’s usually very cheap. Like $10 cheap. However, if you don’t know what you’re doing OR if the water doesn’t totally shut off with the shut offs, it’ll be easier to just replace the whole thing. Two plumbing connections under the sink is easier than rebuilding that, especially if the water is going to be moving while you’re working.