+1 on not cleaning the Model 60. If you find ammo it likes just shoot it. Clean the action of residue every now and then. Rimfire Central has some good tips on lighting up the trigger. Use with caution, and I do not in anyway condone these methods. I used them on my rifle, at my own risk. You make your own decision.
The gun is kind of a pain to clean because of the small bolt and small area and internal parts, but it can be done.
A good air compressor and some ballistol or similar cleaner (foaming or not) works wonders on the bolt area, but be sure to leave it dry, or you will collect more dirt and residue than you want to deal with, and then you will have a far less reliable rifle.
Like I mentioned about ever 3rd box of 500 I clean the action only. I know it sounds weird, but my rifle just shoots good without cleaning. They are great guns, and they just are as mentioned. They are just a great rifle. Especially for the money. Cheaper than a 10/22, and more accurate from my experience right out of the box. You can spend $400 to get a 10/22 to shoot as good as a Mod 60, but then you are not shooting a stock rifle.
I am not trying to start a 10/22 vs Mod 60 debate. Everyone has their opinion, and I will take a Mod 60 over a 10/22 out of the box any day. If you get the trigger down a pound or two it is even better, but then the Mod 60 is not stock anymore either. If Marlin ever got one rifle right. It is the Model 60. I am sure their bolt rimfires are just as good.
Just keep the mag tube and feeder clean, and you will be able to shoot the rifle for years. Probably long after you're gone.