The Nuclear Arms Race -- Need advice

Start at the top, then: Google. Google all those topics you mentioned. You should get enough information to fill out 15 pages easily.
Welcome to A2K, and good luck with the report.

You should use your school's library to search for physical primary and secondary sources. Also, many college/university library programs pay for online access to huge databases of primary sources. Check out your school's library's website; look for a section about online resources, databases, etc. I would NOT trust regular websites as sources for your paper, though, so don't even try it. Really. Use your library.

...Wait, I just realized that you wrote "I'm the OU" and not "I'm at OU", so maybe you aren't a college student yet (thought I don't know what an OU is otherwise). Even if that's the case, still use your local library. Even secondary-source books, which go through the whole editing, publishing, promoting, distributing, public opinion process, are still way better than the Internet. Seriously.

Start with the Manhattan Project. There were good reasons to believe that Nazi Germany was actively working to produce an Atomic Bomb. There was no question that it would be catastrophic if Hitler were to produce atomic weapons before the Allies. Britain and the United States jointly worked to produce an Atomic Bomb in the largest and most secret public works project ever. Neither France nor the Soviet Union were told of the Manhattan Project, as neither had anything to offer and both were regarded as a security threat to the Project. Never the less, Soviet spies were actively collecting every secret they could get their hands on, including the Manhattan Project. Scientists and technicians at Los Alamos transmitted reports and drawings of their work to Soviet spies. Eventually, the Rosenbergs were arrested for giving atomic secrets to Russia. After a controversial trial, the Rosenbergs were executed. Documents discovered after the fall of the Soviet Union confirm the Rosenberg's guilt.

After Hiroshima and Nagasaki, Stalin went all out to produce a Soviet Bomb. The United States was shocked that the Soviets were able to test a nuclear device so quickly, and there was great national concern that Stalin had the weapon we had worked to keep out of the hands of Hitler. In those days the primary delivery system was the long-range manned bomber, and the Soviets had stolen the plans for our Super-Fort (NATO Desg. Bear). The U.S. Strategic Air Command (SAC) was built up even as other portions of the US military were cut back. The U.S. and Soviet Union embarked on a long series of nuclear tests, and that further raised concerns over possible nuclear war. The U.S. developed during this period the first thermonuclear weapons that had many times greater destructive yield than the atomic bomb (1-100 MT v. 10-99KT). The Soviet Union promptly stole those secrets as well, and soon tested a 100 MT device (the largest nuclear explosion ever).

Both the Soviet Union and the U.S. captured essential German rocket scientists at the end of WWII, and both engaged in programs to produce long-range missiles. The old V-2 became much more sophisticated and capable of carrying nuclear warheads that were becoming smaller and with greater yield. There was talk of a missile gap that favored the USSR, though later it was found that if anything the U.S. always had the preponderance of missiles. To offset the supposed imbalance, the U.S. developed the MIRV concept. Multiple warheads would be carried on a single missile at launch, and then independently targeted on re-entry. The Soviet's built their own MIRVs.

The U.S. Navy consolidated it's control of the world's oceans by building atomic powered submarines that could remain submerged almost indefinitely. Atomic powered aircraft carrier task forces allows the USN to remain at sea for long periods, and extends the reach of naval airpower over most of the globe. After the SSN Nautilus, a number of more refined nuclear submarines were designed and built. The Polaris missile could be launched from a nuclear submarine without its ever coming to the surface. The Polaris was nuclear capable. The Soviet Navy developed their own "Boomers" and nuclear powered attack submarines, and the two navies carried out extensive "games" of hide and seek with one another during most of the Cold War which lasted from 1945 through the mid-90's.

The US nuclear doctrine was called the Triad (manned bombers, ICBMs, and nuclear submarines capable of launching MIRVs). It was an expensive undertaking, and was the underlying US strategy for conducting waging a war of survival against the Soviet Union (adopted during the Truman Administration ... it worked).

At the height of the Cold War there were so many powerful nuclear devices in the US/USSR inventories that a full scale launch would certainly have had a catastrophic effect on the world, and was almost unthinkable (see H. Kahn, Thinking the Unthinkable, and On Thermonuclear War). The MAD (Mutually Assured Destruction) concept was accepted by both sides and prevented the outbreak of hostilities that could quickly escalate into an spasmic exchange of two truly huge nuclear arsenals. The Cold War became a series of limited conflicts carried out on the peripheries by clients of the two super powers. The dangers and costs of any nuclear arms race were evident, and resulted in a series of International Agreements to limit nuclear prolifrication and testing. Both the USSR and the US have largely lived up to their agreements, but in the Post Cold War Era some of the old "client states" have ignored the lessons of the 20th century.

Israel may, or may not, have nuclear weapons. They foster the belief that they have a small arsenal, but have never tested or shown them to the world. Israel is decidedly low-key in the nuclear game, and no one seriously regards them as a threat to world peace. India, with Soviet help developed a nuclear arsenal that prompted its old enemy Pakistan to build and test its own nukes. For a long time now the Indian/Pakistani nuclear standoff has worried a lot of folks in Southeast Asia. That threat seems to be cooling somewhat today, but could easily flare up again if radical Muslims were to take control in Pakistan, or if some Indian politician went a little crazy. The DPRK probably does have today at least several Hiroshima yield nuclear devices, though their reach remains limited to the region (USSR, China, ROK, Japan, and perhaps parts of Alaska). No tests of the DPRK devices have been made, nor is there any suitable site for a DPRK nuclear test. The DPRK has a longer range missile that has never been tested, nor even stacked so far as we can determine. Iran is the latest nuclear aspirant, and the they say they are only interested in generating electrical power (nudge, nudge, wink, wink). Actually, there is little doubt that Iran is purposely working to develop nuclear weapons. Their outspoken threats against Israel and support for international Islamic terrorists make Iran a threat to world peace.