So, prior to the start of the 1948 war, the Haganah, Irgun, and Lehi (some of the main Jewish defense groups that were around after the war began) had already begun arming themselves. Before 1948 the arms were coming in from a variety of sources, and they were coming in through organized efforts as early as 1909. Between 1909 and 1913, Jewish settlements in Palestine began to face violence (and be involved in it themselves) over tensions over Zionism, and so began to arm themselves with "5 to 20 rifles per moshava [settlement]", according to its size. Some settlements approved as much as 5 thousand francs for the purchases. The arms purchased came from anywhere one could find, there was no (as far as I'm aware) special group funding their purchases, and no preference for British goods.

This process of arms acquisitions would continue and escalate rapidly. We do know that Zionists, throughout the 1930s, were purchasing arms and ammunition including Lewis guns, but these acquisitions were (again) coming from anywhere they could buy. They were often shipped into the country though, as one incident shows when a barrel filled with ammunition and 25 Lewis guns was accidentally broken after being shipped in to the port of Jaffa, leading to accusations aimed at the British of them allowing a conspiracy to arm the Jews.

I'm going to skip ahead to get closer to the nationhood portion, because I think that's far more interesting and I can give far more detail on it. It's important to note that before Israel declared itself a state, there was already a civil war going on from November of 1947, following the UN Partition Plan being passed in the General Assembly. This would last until the 1948 war began. At the point at which the 1948 war began, the natives were all but defeated, and their social structures had fallen apart. Jewish forces had taken over much of the area of Palestine by 1948, and taken over many cities. This was done with the help of arms that were organized and purchased as early as 1946. British forces, which had allowed Jews to arm themselves to assist them during the 1936-39 Arab Revolt with British and foreign weapons, were now unable to stop Ben-Gurion (Israel's first prime minister, and one of the leaders of the Haganah) from arming Israeli forces with Western arms.

Now down to the nitty-gritty: where did those arms come from, and how were they gotten there? Well, things like primitive hand grenades, bombs, and similar explosives were being produced straight in Palestine, by Haganah forces. By 1935, there were already 100 grenades being produced a day by Haganah forces, at first in primitive conditions and then in a concealed workshop in the city of Tel Aviv. Arms in the 1930s, in addition to a wide variety of other sources, came from Italy, Belgium, and France. This was because Belgium and France had supposedly weak arm controls, while Italy was happy to oppose the British under their current leadership. In fact, between 1935-1937 the port of La Spezia hosted the first course ever for naval forces under Haganah. The agents who purchased these arms would usually have them shipped into Israel in barrels marked "cement", and others would be stored in suitcases and other baggage. Many of the arms were broken and needed repair, and all required maintenance, and some came without ammunition. I unfortunately can't seem to find any information on what models of guns and rifles they are, but I can find what the total count of weaponry Haganah had going into 1948 was, which I'll get to later. The need for these repairs is what led to setting up the underground arms industry that led to the grenade/bomb making, too. By the early 1940s, Haganah could boast 6,000 rifles, 1 million rounds of ammunition, 600 light machine guns and submachine guns, 24,000 hand grenades, and 12,000 rifle grenades. As you can imagine, this was a drop in the bucket compared to what came later.

Israel's arms industry continued to grow rapidly leading up to the 1948 war. By 1944, twelve "institutions" were turning out explosives, detonators, submachine guns, and various types of ammunition, including (by 1948) 20,000 rifle rounds per day. When the 1948 War began, Haganah could now boast 195 3-inch mortars, 682 2-inch mortars, 86 PIAT (Projector Infantry Anti-Tank), 5 old 65mm field guns, 1,558 light and medium machine guns, 11,000 largely homemade submachine guns, 22,000 rifles, 3,830 (probably more) pistols, and 53,751 (also probably more) hand grenades. But even this was a drop in the bucket of what was to come. See, while these weapons were fine for defeating the locals, they were no match for the arms of the invading Arab armies, who had armor, artillery, and aircraft. It was in anticipation of this that Ben-Gurion began the mission I mentioned earlier, to find more weapons from Western nations that could be used. Ben-Gurion had given himself the defense portfolio, and would be acting prime minister of Israel until he was officially elected during the war itself, and so had a lot on his plate. During this period, Israeli agents had gone again to Belgium, France, Italy, and Yugoslavia to purchase more arms. After the British withdrawal, while the Civil War raged and the Battle to Jerusalem was being waged, the heaviest weapons at the Haganah's disposal were self-manufactured 81mm mortars, which were effective, but unsuited for larger warfare as I mentioned. And while arms were still being manufactured and flown in, the Jewish leadership was still unable to get as many arms as it would've liked. In fact, 200 rifles and 4 light machine guns were flown in from Yugoslavia in April 1948, just to help alleviate the shortages. In April, almost all fighting was being conducted with small arms and at close quarters. Urban warfare was common, and armor, aircraft, and the like were a little rare, to say the least.

When the war began, arms were a big deficiency for the Jews. I've already explained roughly what the Haganah could field, and their counts usually dwarfed those of Irgun and Lehi, who were typically smaller forces by far. So the principal sources of arms, post-WWII, continued to be Yugoslavia and Italy, who both showed sympathy for the Jewish cause. However, the crucial arms were brought in from Czechoslovakia, in a deal that was to effectively decide the war by most accounts.

Thanks to the Czech arms, Israelis were able to arm all their forces semi-adequately, and during the first ceasefire of the war the Israelis could consolidate and distribute these arms to a degree that would allow them to fight handily during the rest of the conflict. The Czechs gave the Israelis, in this deal (they were sending weapons throughout the world, really, to the tune of some $12 million at the time if memory serves), 25 fighters (Messerschmidt ME-109s), 200 heavy machine guns, 5,021 light machine guns, 24,500 rifles, and no fewer than 52 million rounds of ammunition. Compare that to what Haganah had going into the conflict in 1947, and you'll see why this was so crucial! The above arms were shipped before or shortly after the start of the Arab invasion on May 15, 1948. They were the Mauser that you mentioned, as well as MG-34 and ZB-37 machine guns, for the most part. Heavy arms remained short, as did vehicles, artillery, tanks, and aircraft. Israel had managed to get its hands on a handful of American B-17 bombers and some C-46 Commando transport aircraft, dozens of half-tracks, and they also managed to buy clandestinely some fifty 65mm French mountain guns, twelve 110 mm mortars, ten H-35 light tanks, and some other assorted weaponry. Almost all of it was sent, and arrived as quickly as possible, but the British blockade lifted on May 15, 1948 was a hindrance that slowed the deliveries a little. Despite all this, the heavy weaponry gap between the sides still hadn't closed, even by the end of the war. The Israelis also managed to get their hands on some Sherman tanks from Western nations (and built a few themselves), though I can't find the source nation, but some of the tanks had perforated barrels and were not able to be reconditioned. And of course, through it all, British arms procured during the Arab Revolt and before the war were also being utilized, but weren't as crucial in the later stages, from my understanding.

This is all the information I can provide, unfortunately, on the arms situation. It's not something I've seen more specific stuff about, but the above should give you a rough idea of the sources of weaponry, as well as the arms Israelis had. I can provide more information on where weapons were gotten after the war ended, as well as Israel's foreign relations, or roughly similar information on wartime weapons the Arabs had (not specific on models and such, sadly). Wish I could do more!

Sources:

Bregman, Ahron. Israel's Wars: A History since 1947. London: Routledge, 2002. Print.

Creveld, Martin Van. The Sword and the Olive: A Critical History of the Israeli Defense Force. New York: Public Affairs, 1998. Print.

Gerber, Haim. Remembering and Imagining Palestine: Identity and Nationalism from the Crusades to the Present. Basingstoke: Palgrave Macmillan, 2008. Print.

Morris, Benny. 1948: A History of the First Arab-Israeli War. New Haven: Yale UP, 2008. Print.

Morris, Benny. Righteous Victims: A History of the Zionist-Arab Conflict, 1881-2001. New York: Knopf, 2001. Print.

Question: are you talking about Israel after the 1948 war ended, or are you asking how they armed themselves during the 1948 war? I ask because "nationhood" can depend on when Israel declared it, or when it was no longer fighting to preserve that nationhood's fledgling identity :).