Welcome to FT!!
As in most cases, what works for one doesn't for the other. There are so many factors to consider, such as price, scheduling, frequent flyer program, etc.
However, just based on product alone, the only true premium economy that flies to TLV that makes sense for you is BA. You can fly World Traveller Plus ORD-LHR-TLV and get it on both legs. Other airlines that fly to TLV and offer true premium economy don't offer it on the TLV leg.
As a secondary, you can fly DL from JFK and fly Comfort+ which is a pseudo premium economy.
As for the best economy experience, it depends on what you're looking for. Few airlines have wowed me in Y. BA isn't bad nor is LX. I'd stay away from LH. I've been fine with UA and LY is also not a bad option in Y.
If looking to upgrade to C on *A, you'll want an airline that'll give you true C the whole way there. UA offers that EWR/SFO-TLV, AC offers it YYZ-TLV, LX usually offers it ZRH-TLV but occasionally subs an A320, and finally, OS occasionally offers it VIE-TLV.
I'd actually lean to UA on this one, but note that it's a very hard upgrade.