Hey yep it can definitely be confusing when you're first learning it. No worries because that's why this message board is here
I would keep the Gap card open but stick it away somewhere safe so you don't lose it. With the Visa thing it actually doesn't matter because Visa is only a payment processing network. They're not the bank. Here's the history of Visa credit cards
Don't worry about the payment networks a card is associated with. What you want is to have is different banks/financial institutions and it you already have two different ones with the Visa and a 3rd one through Gap which is issued through GE Capital. I suppose it may not hurt to get another credit card from yet another financial institution but you want to be careful because if its a temptation to spend you should do it. And you should definitely be able to qualify for some good rewards credit cards despite your age/short credit history!!