travel to middle east.?

I am planning on taking a trip to the middle east as I am lebanese/armenian and I want to take to take a cultural tour of my roots. I am hoping to stop in both arabs countries and israel, but my family tells me that it is logistically very difficult because once you have a israeli stamp in your passport (US) many countries wont grant you entrance, and visa versa. What's the best way (other than getting a second passport to organize this so that I can enter both types of countries? Serious Answers Only. Thanks
I never said that armenia was an arab country, no more than I said israel was an armenian country, I m not visiting armenia during my trip, I lived there for 11 years and my mother was born there. I have never been to israel or lebanon though, thats where I am visiting.

Hi, if you go to Israel first you will not be let into Lebanon for sure.
I have heard in some cases the Israeli government will not stamp your passport, but only in very special cases.
Oh yeah, you can get another passport from the US.

Israel is an enemy country to Lebanon, israel doesnt support travels there.......idk

You can either travel to Lebanon first than go to Israel or ask Israeli customs not to stamp your passport as you want to travel to an Arab country..
Most of the time they will oblige because a lot of businessmen who work in that area find it extremely problematic travelling around the Middle East with Israeli stamps, so they simply tell them they cannot have their passport stamped for work related reasons..
Have a good trip

Armenia is NOT an arab country! You are half Armenian and you still don't know that? and the rest is said by the poeple above me.