It's hard to get credit cards with no (or little) credit history. But, talk to your bank about a secured credit card. You will have to put money in an account to secure the card, but you can get a credit card to start building a credit history. It's not a debit card that takes the money from the account. That account is only there if you default on the payments. You make regular monthly payments just as you do an unsecured credit card.
You can also look into buying a car if you make enough to afford it and have a parent cosign with you. It's a lot easier to get the loan if you have someone with a good credit history also sign the loan. Both parties are responsible for the loan as far the bank is concerned, but you and the cosigner will get it added to your credit history (good or bad).
There are also many things that do not report to your credit if you pay on time, but they will if you fall behind on payments. So make sure all your bills are paid on time, and it will help prevent bad reports from showing up. And don't apply for any card you find an application for. Each application you make, they will pull up a credit report on you, and that will go against you on your credit score. It's called a "hard hit" (soft hits do not go against you).
Bottom line, it takes time. So be patient and pay your bills on time.
I think those secured credit cards are a thing of the past. If you have a checking and savings account and it's been for a couple of years then you should be able to get credit if you earn over $15,000 a year. Sometimes people get a store credit card first and use it for a year and once they increase your limit then you can get other credit cards. Right now some credit cards are asking 0 interest thru 2016 so now is the time to try. If you get refused it's ok, but apply anyway. Once you've opened an account let a few months go by and then check your credit (you get one free credit report per year).
When I was in college and buying books for the final courses I noticed that the school library had credit applications laying out for seniors. Usually they want seniors to buy clothes and a car. Maybe you're too young to get credit (and that's a good thing) so go buy yourself a giftcard (Visa) at any Walmart (or other stores) and use that.
Capital One has been generous towards first-time credit card applicants. If approved, it will be a small line ($300-$500) and probably have an annual fee, but use it every month and pay it off, on time every month, and they will increase your limit after six months, and again in the future.
If you still can't qualify (perhaps even if you can), if you have a parent or an adult who is responsible with their credit, ask them to add you as an authorized user--even if they don't actually let you USE the card. As THEY use the card, it will report on YOUR credit history too. Remember--you want a RESPONSIBLE adult who is using their credit card wisely or their negative history will also report on your credit history, even if you are not legally liable for their debt.
You can also go to a credit union and apply for a small secured loan to help build your credit.
Any card you can get will do. You will need a cosigner until you are 21. Odds are good, you will still need a cosigner after you turn 21, as I doubt you work full time due to college. Part time income does not count & you can't add the 2 jobs together. Read the application form to be sure you qualify. All of them have income and employment requirements.
Try to keep your job as long as you can. Talk to an investment advisor. They (rich people sitting in high places) are making it very difficult and unnecessarily tedious to obtain credit. People you don't know but who know you and possible sources of "income" (called personal business) might be the culprit to this conundrum.
Which credit card you have makes no difference to building your credit score.
Paying bills on time is what builds your score. It makes no difference who you pay the bills to.