Really good question(s)!
This article struck me as reasonable: http://guides.wsj.com/personal-finance/credit/how-to-monitor-your-credit-score-and-credit-report/
Particularly this: "Your credit score (also called your Fair Isaac Corp. (FICO) score) is a three-digit number between 300 and 850 calculated from a formula that’s designed to gauge your creditworthiness. The three main credit-reporting agencies (Equifax, Experian, and TransUnion) buy the formula from Fair Isaac. The bureaus use your personal data and crunch the numbers differently, so your score will vary slightly at each agency. When a lender considers your application for credit, they turn to one (or all) of the credit agencies for your score, which indicates your reliability as a borrower."
Seems like, to me, using one of the three main bureaus is a good place to start (as they all rely on FICO). And while you can work to monitor all 3, just focusing on one may bring some peace of mind!
Do you have a score goal in mind? And if you do (I'm trying to raise mine by 50 points), do you have a plan in place?
You need to get copies of the actual reports, not just the scores, to see what's on there contributing to the score you see....then dispute anything that is incorrect (you'd be surprised at how much old and incorrect stuff stays on the reports until someone disputes them). You'll want to research how long something is allowed to stay on your report for your state, in California, its 3 years for most types of debt...anything older than that can be disputed and removed.
Annualcreditreport.com will give you a free copy every year, be sure you read the screens as you go through it, so you don't accidently opt for something that they can charge you money for....the credit reports themselves should be FREE.