Marlin 336. Lever action. Most were in .30-30 but some were in .35 Remington (that may be the 35 you were referring to in your original post). .35 Rem is a very good caliber but getting hard to find. You likely won't find ammo in EVERY mom and pop store.
If is has no "S" after the 336 it is older w/o the cross bolt safety.
Marlins are FANTASTIC rifles...some of the most reliable and most accurate you will ever run across...and oddly, the most inexpensive.
Marlin is the Kenwood of firearms...solid, dependable, work & sound better than you ever expected
Micro-groove barrels are one thing...finicky about what you feed them as Morris the Cat. You will likely have to try a couple of different manufacturer's bullets to find what yours likes the most. Your best friends will soon be a Micrometer so that you can measure the bullet width of the rounds you will put through it and a notepad to write down your group results.