I concur with DanBell and seau grateau.

Start with a good cleaning/lube/adjustment on all spinning parts: pedal spindles, bottom bracket, wheel hubs, and headset. If they're rough, stiff, sloppy, or noisy: disassemble, clean, repack with new grease, and reassemble with proper adjustment (in the case of loose ball & cone bearings) or just remove and replace (if they're cartridge type).

Thoroughly clean and lube the chain.

Carefully inspect the whole bike for loose hardware.

Check wheels for bent or wobbly rims or loose spokes.

This will all require minimal cash expense and should only take a few hours, maybe one day. It can make a BIG difference on the bike.

Since this is all very new to you, you should get a good book. I like Park Tool's "Big Blue Book of Bicycle Repair," but there are others too.

Once you've sorted out all these minor maintenance issues, you can start looking at upgrades.