As far as the chain goes. It's the most important part on the bike. IMO. It has the most moving parts on it. 588. I use a simple chain cleaner from the LBS and some simple green. An old toothbrush works great at getting in between the plates. I try to clean it at least once a month or whenever it looks like it needs it. I use Finish Line wet lubricant for extreme riding conditions. There are all kinds of lube. That's just the one I like cause it works good in cold temperatures. I use a Park tools chain measuring tool to check the chain stretch and always replace the chain as necessary, usually about twice a year. (I'm riding about 5k a year). That will save you from wearing out the teeth on your cassette.
As far as tools go. I just buy whatever I need at the time. Over the years I've accumulated quite a collection of bike tools. My last purchase was a set of cleaning brushes from Park tools that do a great job of getting into those tight spots that other brushes can't reach. You learn as you move along. After a few years you'll have the bike set up just like you want it, and be confident enough to fix whatever it needs. Asking questions here is a great start. Good luck.