If you haven't had a credit card before, you'll need some credit history with another issuer before target's bank will even consider you for a redcard.
Years ago, store credit cards were the easiest ones to get for people with no credit history. That's no longer the case. Consider the debit redcard, but you'll need to bring a paper check to the store (or apply online, which won't give your TMs any brownie points/recognition for signup). Just remember transactions on the debit card don't clear instantly. You might make a purchase with your debit redcard on Saturday but it might not clear your account until Tuesday or even Wednesday. It's more like writing a check in that there's some float time, just be careful so you don't overdraft your checking account.