I've become fairly knowledgable on the subject recently. I got fairly screwed during a student loan consolidation process where I had something like 8 different student loans, and I think the Hutchins loan at Wake or something didn't or couldn't get consolidated and I didn't know until some debt collector called me up and said my student loan was delinquent like 9 months.
The main factor is to not have any 30 day + delinquent credit card, student loan, car payment type payments for a period of 24 months. After 7 years any late payments are completely wiped off, but its much more heavily weighted towards the first 2 years. Utility bills shouldn't show up on credit reports, unless there's like a lien or a judgment against you in a public record. Paying phone bills/utility bills on time doesn't show up on your credit report. So if you have a choice and are tight one month, prioritize credit card/studentloans/car payments over utility/phone/internet bills.
I would advise doing a one time credit report at equifax or something BUT MAKE SURE TO CANCEL IT. The sites charge you for 2 seperate things, usually $14/mo for their service and you get dinged $7/mo for something called triple advantage. Alternatively you can go to a website called quizzle and in a few minutes get a good free estimate of your score.
I applied for a credit card recently and the score it said when I applied was about 40 points higher than my equifax tells me, and my quizzle was about 40 points higher than my equifax told me, so quizzle may well be more accurate.
I would get one of those crappy cards with shitty/no rewards. Generally you can double the say $500 credit limit to $1,000 within 6 months or so, but you are paying a hefty usually like $60 fee. Ya keep the card for a year or two max, and by then your score should be strong enough to get a capital one card or something which will give you some rewards and like a $2,000 limit with about a 670 score. A few years of that and then you can likely qualify for the real $5-10k limit cards, which are nice to have in the case you lose your job or something and want some security of having the ability to draw on 6 months of living expenses or so.