I'm 22 and recently got my first credit card so I know exactly what you mean! Here are some things I was told about or kept in mind when I applied for my first one-
It's easier to get a card if you have a financial relationship with an institution; I've been using the same credit union since I was a kid so I applied there. I actually had to call and check on my application because it was rejected twice. However, I had literally no credit history at the time and they just needed to verify my identity.
What you want to look for is a low interest rate. I have also heard it can be helpful as well as if the card as a period of time with no interest at all - I have heard conflicting advice about carrying a balance during this time to up the score (DEFINITELY not sure of the merit or value in this, can anyone confirm/deny?), but you should also keep in mind that credit usage is a factor in your score. For example, if you have a card with a $1500 limit and you are using $1300 of it every month, the bank may see you as a risk and not want to up your credit limit.
Look for a card without fees and definitely read the fine print on anything before you sign. I highly recommend going to your local bank or credit union and asking to meet with a banker to discuss credit options; they can often help you narrow down what you should apply for and would be able to get.
Now, many mystery shoppers seem to apply for high rewards cards (ie spend $xxxx in the first y months and get z cash as a reward), but be careful that those cards don't end up costing you in fees later. You can close the credit card, but you don't want to be opening and closing lines of credit as I've heard that can have a negative effect on your score. The Mint app can recommend offers with cash back.
FINALLY: definitely keep an eye on your score and reports - you might already know that you can get a free report 1x per year from each of 3 institutions that gives a score, but apps or websites like Mint and Wells Fargo online banking can give you an updated score every month and send you an alert when they have it. Read your entire statement every month to catch any fraud or mistakes.
TLDR: Read the fine print. Don't use all of your credit every month. Speak with a banker for expert advice. Apply at an institution you have a relationship with. Check your score and statements often. Get a low interest rate, avoid fees, and look for $ rewards for spending a certain amount. Also I'm only 22 and tried to note where I wasn't sure of info so you can do more research or others can chime in.
I hope more shoppers share their experiences with using rewards cards and what they look for!!