When looking for a solution the first thing should be to identify the problem. So if we are looking for a solution first we need to understand that the conflict is not between the "Palestinians" and the "Israelis". That description is just an attempt to mislead the public.
The real conflict arised between the Arabs and in more general the Muslims and the Jews. To this day many of the Arab and the Muslim countries don't recognize the existance of Israel in any borders.
Historically Jews who lived in Arab and/or Muslim majority areas were usually regarded as second-class poeople. All kinds of restrictions applied to them and they had to pay a protection call Jizya (along with the other non-muslims). Even that did not fully protect them as the history of the Jews unde Muslim rule includes many pogroms.
The Jews were considered inferior to the Muslims.
The situation varried between territories and rules, but it had a general similarity throughout the time and various places.
The situation was similar in the area called Eretz Israel (the land of Israel) that was renamed by the Romans to be called Palestine.
The Jews who lived ther throughout the centuries have seen attrocities (nice word for pogroms) perpetrated by the Muslim population. (Also by the visiting Christians as well, but that's less relevant for this discussion.)
In the 19th century Jews started to return to this land in larger numbers escaping the pogromgs of Russia and Eastern Europe and finding refuge in the land.
More and more Jews arrived many with an ideaology of equality among people. These people were usually quite poor, but with the help of some wealthy Jews they could purchased land and start to build strong communities. The economic situation of the area improved which brought in more muslim arabs from the neigbouring territories. Namely Syria and Egypt. The childern of these people started later - in the 1960's - call themselves Palestinians.
Who is fighting agains Israel?
It is quite obvious that besides the Palestinians many arab and muslim countries are also fighting agains Israel.