You came to the right place, Gary. Welcome to the club, literally!
There are plenty of people here who will gladly clue you in, and if you can make it to one of the many rallies, you will get lots of hands-on help understanding your new-to-you coach. That said, expect many replies here.
For my part, I suggest:
Understand the difference between chassis and coach (house) batteries, and how your coach ones are wired together;
Keep the battery top and posts/connections clean and corrosion-free;
Keep any batteries that require water topped up to 3/8" from the bottom of the cell ports with distilled water;
Don't allow the voltage to drop much below 12 (frequently check your panel when dry-camped);
Don't drive off from a dry-camp of any length expecting your alternator to recharge everything - you will shorten the life of your alternator,
and related to that, keep your generator well-maintained and ready to recharge your battery banks while dry-camped;
If you can afford it, get a 100 watt solar system installed - it can go a long way toward maintaining your system, but isn't absolutely necessary;
Buy a Battery Minder or similar brand of maintenance charger for keeping your batteries charged and/or equalized during storage, esp. if you don't install a solar setup, or if you store the coach under cover where sun can't get to a solar panel.
I know that's a bit more than 3 or 4 things you asked for, but you need to do more than 3 or 4 things to take care of your batteries.
As to the hydrometer, I have one, but haven't used it for many, many years since that's how long my batteries last. If you don't know how old they are or how well your batteries have been maintained, getting one would be a good idea. Having a good quality multimeter would be a good investment as well. Many people also use devices for "automatically" topping up battery water, but I personally can't justify the cost, and prefer the old fashioned method which isn't all that difficult a task every few months.
Sharing your excitement,
-Joel and Lee
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