New to the bike world need some input
Looks like a nice, well maintained bike, however its 1980's or 90 era geometry means its not worth pouring money of a new group set into making it better.
From a learning experience on bike maintenance you may be better to get the bike running smoothly by working on what you have, replacing bits that are worn might be a better starting point. If you dead keen on the new group set, be aware its still an old frame so the geometry is 'wrong' by todays standards.
My approach to this bike would be :

Service headset and wheel bearings, clean and lube chain and lube shifter and brake cables. Check the tires for damage, and brakes are working well enough. Get out and ride it before spending more money.

If I was enjoying the bike, and it was still a bit rough....

Check derailleur hanger alignment
Check Bottom Bracket for wear, replace if needed
Replace shifter and brake cables - probably inner and outer, but could be convinced to keep outers if they not showing signs of age.
Check chain for wear, if worn, replace chain and rear cassette.
Check chain rings - from picture they look OK, but hard to tell.
Check the wheels are true.

All these things are covered on this site in various questions, and Parktool has a great &quot;how to&quot; site for DIY maintenance. You will need some tools, but a you can get bike tools kits that are good enough for a careful DIY mechanic, containing all you will need, especially for this era bike, quite cheaply.