You can divide the six main missile programs into two categories. One are "purposefully redundant approaches to the same task." So Atlas and Titan are both heavy, long-range, liquid-fueled ICBMs. They are deliberately trying to solve the same problem, but they had different teams working on them. Similarly Redstone/Jupiter and Thor were liquid-fueled IRBMs.

The other two major rocket programs being pursued were both solid-fueled, but to different aims. Minuteman was a solid-fueled ICBM, Polaris was a solid-fueled SLBM. Both were tricky technical problems with different dimensions (Polaris had much shorter range and had to be much smaller and also be able to be launched from an underwater submarine).

The intent was never to push all six into production. The intent was to say, "OK, now that we've looked at six different approaches to nuclear delivery by missile, which two are the best?" And then cancel the rest.

But after the Soviet Union beat the US into space with Sputnik (October 1957), Congress and the military wanted... all of them. And soon. Eisenhower felt unable to resist the lobbying from Congress, the military, and the public. All six missile designs were rushed into production and some even into deployment, even though some of them were terrible (Jupiter was just a bad idea, and the deployment of them to Turkey was a proximate cause of the Cuban Missile Crisis; the first generation of Polaris missile warheads were likely to be duds).

Even focusing on the "main six" understates the issue. There were whole other families of missiles being pursued simultaneously, like Regulus I and II, Snark, Rascal, and so on. Some of these were rushed dangerously into production when they were very untested, as well.

Eisenhower's feeling of a lack of control over this is in part what contributed to his famous "Military-Industrial Complex" speech in 1961, in which he warned that the forces behind the arms race were taking on a momentum of their own.

Several reasons. One is that there are different organizations sponsoring development. Another is that there were different missiles of different designs which were developed on different time frames, and there was some overlap. To avoid having capability gaps at the time they pushed pretty hard to ensure that they had follow-on generations ramping up as the older generation was plateauing, which naturally led to quite a bit of overlap. On top of that, you do have examples of parallel program development as a means of risk mitigation, which resulted in multiple missiles coming online at around the same time in some cases. And, of course, there are also different missiles of different capabilities, as is the case for Thor and Atlas. Thor and Jupiter were intermediate range ballistic missiles, not ICBMs.

In the early years this can look like a mad scramble due to the sheer pace of progress and the rapidity of programs spinning up, reaching fruition, becoming obsolete, and spinning down. For example, Atlas as an ICBM had a less than 10 year service life because it was surpassed so quickly. The Titan missile program began as a backup ICBM development program for Atlas (although initially both rockets had fairly similar designs, also similar to the Soviet R-7: two (ish) stage kerosene/lox fueled rockets). Both Atlas and Titan came online in the late 1950s and were built out hurriedly due to fears of a "missile gap" though in reality the Soviets were pretty far behind at the time.

In the mid '60s the Titan-II was developed, which was a second generation ICBM that used storable propellants and could be kept on alert 24/7 in a hardened silo, dramatically increasing the capacity to credibly launch a retaliatory strike. The older generation of LOX/Kerosene ICBMs were then retired (around 1965). This was a case of sheer technological advancement and obsolence at play, once the Titan-II entered service in 1963 there was no reason whatsoever to keep the LOX/Kerosene ICBMs in service.

The next generation of development was switching from storable, liquid propellants (which were problematic in many ways) to solid fueled rockets. That's where you get the Polaris missile and the Minuteman. When the Polaris came online it replaced and obsoleted the Regulus cruise missile and ushered in the modern age of submarines as a highly survivable long range ballistic missile platform. The Minuteman came online in the mid 1960s and served alongside the Titan-II as a ground based ICBM. One of the reasons why the Titan-II wasn't completely obsoleted is that it still had a greater payload and was capable of delivering a larger warhead (9 megatons vs. the Minuteman's 1.2 megatons). Also, there were some development hiccups with the Minuteman which would have given people pause if it were kept as the sole ICBM in service.

Then you have a lot of interesting things start to happen in the late 1960s through the 1970s and you have a very complicated dance involving technological development and geopolitics. First you have massive increases in the sophistication of ICBM guidance systems, due to the rapid rise of the electronics industry and of spaceflight, more experience with satellites and spacecraft, and so forth. One result of this is that ICBM re-entry vehicle (warhead) targeting becomes much better. This leads into the development of the Multiple Independently-targetable Re-entry Vehicle (or MIRV) concept, first realized with the Minuteman-III in 1970. Instead of one megaton or multi-megaton nuke hitting some significant fraction of a kilometer away from some "really valuable target" and ensuring it gets wiped out through the sheer size of the bomb you have a handful of smaller (several hundred kiloton) warheads which are much more precisely targeted. The result is that you can achieve even greater and more certain destructive impact with fewer missile launches and less total megatonnage.

Meanwhile, at almost exactly the same time the massive increases in electronics sophistication made it possible to develop anti-ballistic missiles. Now, keep in mind that at the time these systems were nuclear warhead based, they were intended to guide a low yield warhead near enough to an incoming warhead and detonate at very high altitude. A detonation of a, say, 10 kt warhead at 20km altitude would have minimal destructive impact on the ground and produce a comparatively small amount of radioactive fallout, and would produce vastly preferable damage compared to a 500 kt (or 10 megaton) warhead detonating near the ground.

Anyway, the development of MIRVs and ABMs set off another rapidly escalating arms race since these systems were somewhat naturally antagonistic. With MIRV technology you could flood a target with a high number of warheads plus you could add in "penetration aids" such as inflatable radar reflective or infrared warm decoys, chaff, etc, etc. In the US vs. USSR dynamic if one side wanted to maintain a credible "Mutually Assured Destruction" deterrent force that meant they needed to not just make use of decoys and whatnot but needed to create a deployed force that had an overwhelming number of warheads so that even with a reasonable level of attrition due to ABMs enough would get through that it would be devastating. Which meant on the other hand that if you wanted an ABM system that was worthwhile you had to scale it up in concert to overtop the decoys and penetration aids and the attempt to overwhelm the system, and so forth. So it becomes quite rapidly a game of ridiculous and excessive oneupsmanship. Both sides saw that the situation was primed to rapidly spiral out of control and become not only excessively expensive for each side to keep up with the other but also significantly risk entering a stage of destabilization where the risks of an actual nuclear exchange became higher. So they signed the ABM treaty, which put some limits on ABM systems. Even so, the 1970s and 1980s saw the transition of nuclear weapons delivery systems toward primarily MIRV capable launchers.

Then you have the various other arms limitation treaties which resulted in the US and the USSR/Russia stepping back a little from pushing everything to the limits of technology. For example, the "MX" missile program which was intended to replace the Minuteman was retired after a fairly perfunctory and limited service life. Many land based ICBMs have been "de-MIRVed", being pared down to just one warhead even though they would be capable of supporting more, etc. The Titan-II was eventually retired in the mid '80s as it finally outlived its usefulness.

Hopefully that provides some context as to why at any given time there has been a mishmash of different ICBMs in the US arsenal, and why especially in the early years it seems like there was an especially large diversity of different ICBMs (because there were, but for good reasons).