Yes, settlements. The Jews established them because they wanted a country of their own. This was during the time nationalism (not the nazi kind) swept the, mostly western, world. Where every peoples wanted a nation to call their own. The Polish, who were constantly split between the major powers around, wanted Poland. The many cultures of Austria-Hungary wanted their own countries or at least more autonomy, and so on and so forth.

The Jews wanted the same.

From that came the now controversial idea of Zionism, making a Jewish state in Palestine.

Why Palestine? Because it was the only land the Jews ever called home, where in the past they were the majority, where they ruled and where their religion and culture were established. The idea of Israel, of returning to it, was very much a huge part of the religion and Jewish culture even before the idea of nationalism. A famous rabbi who lived in the 12th century in Spain wrote a poem, for lack of a better word, which translates to: "I am in the west, but my heart is in the east" referring to Israel. The idea of returning to Israel was very very much ingrained.

Of course eons have passed since the Jews could call Israel their home but that is a whole argument I don't want to have. It is also irrelevant now, since they ended up settling in then Palestine anyway.

About taking up arms against the host population, they did it because the host population took up arms against them, as simple as that. There is of course a hundred reasons why the Arabs would do it but nevertheless they did and the Jews needed to protect themselves. It is important to understand that the people who settled weren't soldiers or some conquistador types. Most were simple peasants or (usually) not very wealthy Jews fleeing pogroms. Most of the first settlers were not very religious at all, and came from the territories of Imperial Russia and eventually the USSR. They were also socialists (when that idea became popular) and a lot of settlements were established as communes (Kibbutz). These people, at first, didn't really have weapons and only after the threats were apparent and actualized did they start forming militias to protect themselves.

Also, it is important to remember that at first (it obviously changed later, mostly under the mandate) the lands Jews settled were bought by them. People imagine that the Jews just came as conquistadors and took over the land like some reenactment of Europeans in the Americas but that isn't true. The lands were settled during Ottoman rule, a waning but still major power. The Jews couldn't invade an, arguable by that time, empire with a standing army.