That’s likely older than 2010 from the look of the crankset and derailleurs (edit: googled some 2010 photos, they look similar actually. Looks like it might be this model).

Doesn’t sound a terrible price but they were in fantasy land at 550. Whether 300 is ok depends on the rest of the groupset. If the cassette, chainrings and shifters all need replacing then it’s a ripoff.

A new chain is one thing but if the cassette is still the one that has been on it since new that’s likely done (50-60 for a new one) and you’ll only find out by riding it and putting some pressure through the pedals. It’s hard to tell worn teeth by eye, but have a look at some pics of new ones and see if the teeth on this at both ends don’t look too sharktoothy
Crank the pedals backwards by hand and see if those bearings feels / sound smooth or gritty.

Make sure the cables look ok and brake pads aren’t completely worn out and brake levers return cleanly and don’t stick. See if the wheels are true by spinning them by hand and seeing how straight they run through the brake calipers. Try to wobble the wheels laterally to make sure those hub bearings aren’t worn out (not a perfect test as they can just be badly adjusted if they are cup & cone bearings)

Hold the back wheel up, give it a good few rotations of the crank to get the wheel spinning at a decent speed and then stop, letting the wheel coast. Make sure the chain doesn’t sag on the top run when you do that. Usually means the freehub will need cleaning out or even replacing in extreme cases.

Looks like it has 9 speed Tiagra (if that ebay link is accurate) shifters with the gear cables that come out horizontally rather than being neatly run under the tape as all the more modern ones do. That’s actually a good thing for the longevity of the gear cables.

Giant make decent bikes. The Avail was aimed at women but there aren’t big differences (and you might be a woman but I assumed not based on it being a father’s bike) and colour is what I always look for first in a bike.

You know you’ll need cleated shoes (SPD-SL) for those pedals?

Get a bike lock that resists angle grinders.