Here's a sticky on the forum that will give you info on working on just about any part of the bike. Just look through the maintenance ones. I like Sheldon Brown(RIP) and Park Tools both very good.
As far as tires go for me when they start getting thin I start having punctures and then I replace them. I'm kind of a anti lube guy for chains because they pick up so much stuff. I wait until it sounds like you have a little bird following you around and and then light lube and wipe down ride until it happens again(couple months) and so on. If the lube did not quite it down it can be the rear derailer rollers that the chain threads through. I've had those get sloppy and start chirping when I'm shifting only.
The thing you want to watch for in the chain is stretch. One it stretches it will wear both the cassette and chain and you end up replacing both which is pretty pricey. On average I replace the chain 2 times a year (Nov and March for weather) and am very careful not to cross train, big ring in the front and back or small ring front and back, this will wear both chain and cassette quickly and start causing shifting problem.