I've rented games to (three different) offices, and about to put one in a personal home for the first time. I think $200-$300 a month is the right amount for a modern game (maybe less if an EM). I would try to charge more if it was getting played more than 1000x per month.
In three of the four cases, the people were either friends, or friends of friends. (In the other case, it was a random office, and I had to consistently bug them to make sure I got paid).
I left the keys with the machine, and showed them how to remove the glass so they could do things like fetch stuck balls or replace a broken flipper rubber.
I would also advise that you do this only within a short distance of your home...and to make sure that you coordinate upfront when both parties will be available for repairs. One office was 20 minutes from my house (which always felt too far...basically an hour trip just to replace a rubber or solder a single wire). On top of that, they were only open from 9-5, so I literally had to skip out on my real job to go make repairs. My longest running office client gave me a keycard, so I would do repairs at 11pm or whenever was convenient for me.
The biggest issue is moving games, and this is probably dependent on each person. I know this isn't the going rate, but even if someone paid me $50 an hour to move my own games, it wouldn't be worth it to me. I'd value that time somewhere closer to $75-$100 an hour (for me) because moving machines is the worst thing about pinball. So...take that into consideration.
I always tell people that they need to be willing to keep the machines for 3-4 months. (You could allow swaps earlier than that, for a fee).
Also I'm going to take you to task for referring to pinball machines in personal collections as "investments". They're not investments, in the same way your car is not an investment. Now, if you want to buy a bunch of cars for the sole purpose of renting them out to strangers, then those are investments.
If you have a machine sitting in your basement, that's a toy. The value might go up or down over time, but that's no different than any other object in your house. If you start using it to make money, then I'd say it becomes an income generating asset.
You can definitely make a little money off of pinball, but it's a lot of time & effort. It's certainly not better a better hourly rate than a good paying job.