You can get “specialty” guitar cleaning polish at pretty much any music store. I don’t know the difference between them and other cleaning products you might already have though.
You’re going to have a lot of gunk on the frets and fretboard. When you go to clean that off, just be wary of any cleaner that’s abrasive or has chemicals that are harmful to wood.
Rusty parts, I like to use naval jelly - awesome pink goo that you can get pretty much anywhere. Dissolves rust and is gentle on the base metal. And this is your opportunity to clean up dust around the bridge, pickups, and nut.
Also, if you’ve been playing the same strings for 10 years, you’re going to think you got a whole new guitar when you put on fresh ones.
They’re fine and clean well and disposable afterwards. I have a friend who swears by lemon oil for the fretboard, but I’ve found that’s only useful on the more uncoated / porous type of boards.