The credit card limit depends on your annual income and creditworthiness. Usually banks look at an applicant’s credit history to determine the consumer’s creditworthiness. But since you have no credit history the main factor will be your annual income. No one can tell you in advance what decision the bank will make, but the higher your income is, the higher your limit will be.
With a cash back rewards card you can get the usual 1% cash back on all purchases and maybe more in particular categories depending on the credit issuer. For example, Discover it® Student Cash Back offers 1% cash back on all purchases and 5% cash back on particular purchases that change every quarter. Also, the card has low APRs and does not charge an annual fee.
If you are approved for a card, it may take a week or more for the card to arrive in mail. As you activate the card it is ready for use. All in all, it can take up to 30 business days to get approved and receive your card.