First off, Mazel Tov on your upcoming Chassanah. It should be b’sha’ah tova umutzlachas.
Now to the issue you ask, I totally agree with MM. I made a huge mistake about buying my electrical appliances in US. They can definitely be bought here and that will solve your issues with luggage space for that. Plus you can start with a few basic things and decide what you need more as you go along. A simple hand mixer plus a food processor and possibly an electric kettle are starters. You will probably also want a toaster oven or sandwich maker and maybe even a microwave. You could possibly bring an iron with you but make sure it’s 220.
As far as dishes, for sure don’t waste time (unless you can put it in someone’s lift) to deal with that in America. If you’re going to be here for just a few years, leave whatever you get for presents somewhere over there to use when you go back to the US. If you think you might be here permanently, then either find someone who is making a list (see my idea below) or plan on buying fancy dishes or Corelle here. I think there is someone in Har Nof who sells nice dishes, plus there are tons of stores opening up everywhere with these kinds of things for sale. Just remember that some of them can crack in the shipping process, so it’s not really worth it to ship.
As far as a lift, you could contact Nefesh B’Nefesh like I said to see if they could help with people who are making aliya soon, or else google aliya/lift/shipping container, etc, different combinations to see if you can come up with any info. Keep in mind that it does take time for the shipment to get here, so you have to already be shipping the stuff now for it to be here in a couple of months. You could always make a note in your invitations for shower/chassanah that your plans are to be in EY for a few years/indefinitely (whichever applies) and that cash gifts would be appreciated to help defray the costs of getting the things here or else the gift should be easily packed into a small place.
Oh, and Turkish Air is a good idea also, but still compare prices. I doubt you’ll be buying one-way tix and also you’ll be coming back to the US for holidays, so you’ll take nearly empty suitcases and bring them back full each time.
Hatzlacha on getting everything ready to come here. If you can get my email from the mods, I am over here and can give you info on stores/people selling things if you want more details.