The 10/22 is the most popular 22LR for a reason.
The weak points of the 10/22 are the Spring, firing pin, and the mags.
Learning how to disasemble and clean a mag would be key to keeping one running in the field for a long time.
When I was 18, 27 years ago when I was able to earn $138.00 home for the summer from school I bought a 10/22.
I have put 10's of thousands of rounds through that gun and still continue to do so, I have added two others to the stable.
I think the gun went 5 years of shooting before I was willing to disassemble the gun and fully clean it.
The first has been apart many times and as you know from yours it is a simple design and a blade screwdriver on a leatherman or swiss army knife easily takes down the gun and clean out any muck or mud that gets in there. But dedicated tools would be better.
To keep a 10-22 running in the back woods a small kit containing:
Spare firing pin,
Spare spring / op rod
Leather man or swiss army knife
Small punch to get the rolled pin out of the bolt to replace the firing pin.
Second rolled pin
Extractor
Allen wrench (for the barrel and the mag)
Old tooth brush
Bore Snake
Small Jar of grease. Auto guns like lube.
New spare mag.
The small container is needed to hold parts as you disassemble in the field and keep track of them.
If you get a small water proof container that holds all of this it will weigh only a few ounces and can be kept in a day or back pack.
For about what I paid for my original 10/22 you can put together a small kit with the all the needed parts, tools and grease to keep one running for years out in the deep woods. ( I have a small Jar of RIG grease I use for all of my auto guns and that Jar has lasted 7 years and It is still 3/4's full. A little dab on a Q-Tip or the tip of the punch or allen wrench will get the grease where you want it.) The grease can be used to lube and for corosion protection.
I would go with grease as a little goes a long way, and a spray can of oil can loose charge and then be useless for further uses and you tend to over lube with spray making cleaning needed more.
So far I have not broken any of the parts I have listed on any of my 10/22's, but I did loose the extractor for a week in the garage when I used a tooth brush to clean the face of the bolt and knocked the extractor out and took a while to CSI the floor to find it.
I have no experience with the S&W M-15 except that when I looked at one the plastic stock seemed weak and flexed as I put it to my shoulder.