What's a good credit score for a college student?
I've seen some discussion of credit cards/scores here before, so I thought this might be a good place to get some advice. I'm a junior in college, and I recently checked my credit score with a site called Quizzle. I didn't really know what to expect, but was a little surprised that my score was in the 690s. I kind of thought it would be higher, but I realized I don't actually know what would be considered good/normal for someone who doesn't have a lot of credit history. I'm considering buying a car soon, which is why I started thinking about this (even though I would definitely pay cash for the car).
I've had a one credit card for a year and a half, which had a credit limit of $500 for a year. I called 6 months ago and asked for an increase, so now it's at $1500. My savings total about $16k between savings and checking accounts, and while attending school I pay for all expenses that aren't rent (utilities, food, clothes, etc.). I've never made a late payment for any bill, and I always pay off the balance in full. For income, I have a part-time job where I could net anywhere from 3k to 10k in a year depending on my schedule.
One thing I didn't quite understand was a second card listed on my account. I do have a Gap Visa with my name on it, but the account is definitely my mom's and I was fairly sure she just set me up as an authorized payer so I could have a card for some expenses when I was in high school. I no longer use it ever, and I don't think she does either. The credit limit is considerably higher than my card ($6k), and the highest balance shown for ever being on the account is $5900.
Since it's my mom's account, I have no idea if the card carries a balance, if late payments have been made, or anything. Could this be affecting my credit, or should it? I haven't asked her about it yet, as it's kind of an awkward subject and I'm not really sure how it all works. I've heard authorized payers don't affect or build their own credit if it's not their own sole account, but is that true?
Any advice would be appreciated, especially about whether my score is good/normal/concerning, or things I should look out for/do to improve my credit score or correct any issues.