New tires are the single best upgrade you can make to a bike so get some online for your money and don't cheap out.
The other thing i'd suggest is some pinned flats or spd pedals. I have pic related and like them a lot. Much better than your current style and i wouldn't be surprised if those bearings were shot.
Spin the wheels, if the bearings are rough in the hubs or there is any side to side play, service them. If they are not round, get them trued. Servicing the hubs is something you can do yourself with some tools, but trueing them is harder.
Shift to your smallest chainring, take the chain off the chainring, and spin the crank. If it's rough then look into replacing the bottom bracket. That's not very hard to do.
If you want to improve the braking, get some Kool Stop pads. If you want to improve it more, get new cables.
Get a chain-wear tool and check for chain stretch, replace the chain if you need to.
Don't do too crazy, if you actually get serious about mtbing you'd want something more modern and if you want a really good commuter you'd want something with a rigid fork. It's an ok bike though. Worth buying tools and learning/ attempting repairs for imo because it's not a biggie to fuck it up and getting a shop to work on it you'll quickly exceed it's value in labour cost.