I’m an user on my father’s Citi Premier. I would consider using that however then he gets all the points 
. I would also have to do a bank transfer to pay the balance on his card.
. I would also have to do a bank transfer to pay the balance on his card.
Sounds like a Citi Premier of your own or a Chase Sapphire Preferred would be ideal. On the surface, an Amex Gold Charge card would be great and Amex is somewhat commonly accepted but you wouldn't get bonus categories for non-US locations. You really do need a Visa or MasterCard in Israel. Discover acceptance is going to be somewhat low; the network wasn't even available there as recently as 4-5 years ago.
With the categories, I think those are your two best options for cards. Plus, if you want to travel around Europe or elsewhere by air or want to come home for holidays both points programs transfer to Air France/KLM and FlyingBlue still considers Israel to be "Europe" for all intents and purposes when you price out award travel. That said, it's possible that you may want to consider the new Flying Blue card from Bank of America.
Have you tried the pre-qualification pages for Citi, Chase, and BoA? I know technically they shouldn't market to you before you're 21, but since you do have established credit it doesn't hurt to try. If nothing else, the worst you'd have to lose is a HP and a little pride if turned down for one of those cards.
Edit: Also, you mentioned paying off the balances weekly. Are you letting at least one of those cards report with a small balance when the statement closes? If they're all reporting $0 on your credit reports, you're likely missing some points since not using your credit at all (as it appears on your reports) is riskier than managing your credit cards by using them and paying them (which would be shown by letting at least once balance show on your reports at all times).
