I'm not a mechanic, just a rider but I do have some advice for you if you are just starting out...;o)

Learn to clean your bike well. Google bike cleaning and you will be directed to some websites that will tell you how.

Keep everything lubed well. Especially keep your chain clean and well lubed. Again Google will show you all the points on your bike to lube.

Keeping things clean and well lubed helps keep repairs down.

Learn to fix a flat first thing and get a tool like Quikstik (REI) or some levers. Get everything ianjk MrColsen lists and some rim tape, too. Alot of people swear by Velox. I just tried Pedros it seems OK and the cheap stuff from Nashbar seems to work alright, too. If you are like most people flats will be your #1 repair priority. Probably after that learn to use a spoke wrench to true your wheels. Learn to adjust the brakes. All the metric allen wrenches will see alot of use.

A good repair book helps and the Park tools website is helpful, too.