below are countries that can avail visa upon arrival:
Andora Germany Monaco Switzerland Austria Greece NetherlandsUSA
Australia Hong Kong New Zealand Vatican
Belgium Ice Land Norway
Brunei Ireland Portugal
Canada Italy San Marino
Denmark Japan Singapore
England Liechenstein South Korea Finland Luxemberg Spain France Malaysia Sweden

If country not listed above, they must have visa prior to their arrival.

Israeili stamp is not a problem as far as i know and as what u said, immigration is ok with it as well.

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"Ask the Lord to bless your plans and you will be successful in carrying them out." - Proverbs 16:3