AA and Alaska are the two programs left that are mileage based and work out well for leisure travelers. Both have partners that can get you to TLV (thinking BA). You'd come pretty close to having 25,000 AA flight miles (three LAX-ORD trips bring in just less than 3,500 miles RT and TLV via LHR easily 15,000 miles round trip), so you're right on the precipice of having AA elite status. That comes with preferred seating and 25% extra miles.

Free international upgrades at that level just don't happen, and even domestic upgrades, which you will need to support if they are over 500 miles, will be tough with two tiers above you (Platinum, EXP). You can upgrade with a combination of cash and miles if the inventory is available (and that's a big "if" as you'll be competing with higher status flyers).

As Delta awards miles based on spend, that's a tough program for a leisure flyer to rack up miles, just like UA.

I don't have any airline cards. The best value there is the signup bonus which may give you enough miles for a free domestic trip. My primary cards are three hotel cards where I get excellent value (for instance, a $300 hotel night based on $8,000 in spend, or $4,000 in airline tickets at double points, better than most cash-back cards when you sort out the value).