These are all processors based on AMD's previous generation Bulldozer cores, which were generally considered a failed architecture from them. AMD had decided back in 2011 to go with an architecture that was dependent on more cores rather than faster cores to gain performance. This turned out to be a big mistake, and too far ahead of its time; Intel went with fewer cores but faster cores which turned out to be the right decision. AMD was stuck with this architecture for the next several years, with only minor tweaks to improve performance, but still falling behind Intel. This all changed in 2017, when AMD introduced their new Ryzen architecture generation. Ryzen gives you faster cores, but also keeps the emphasis on more cores too.
That's the history of AMD's evolving architecture. How does it affect you in the real world? As I mentioned these are all holdovers from the previous Bulldozer architecture. So they have lots of cores, but the cores are low performance. Two of them have been updated to use on the same motherboards that Ryzen processors use, the AM4 motherboards: A10-9700E & Athlon 950, both called "Bristol Ridge" architecture. Bristol Ridge is a tweaked and upgraded Bulldozer architecture, same cores, with a new RAM controller designed for DDR4 RAM rather than DDR3. The other two (FX-6300 & Athlon 845) are just old-school Bulldozer for the older motherboards using DDR3 RAM.
The A10-9700E is the only one with built-in graphics. AMD graphics are actually pretty good, based on Radeon R7. AMD graphics has been consistently much better than Intels for all of these years, even while their CPU's haven't been. It also uses the modern AM4 motherboards with DDR4. The Athlon 950 also uses the same motherboard and RAM, but it doesn't include the onboard Radeon R7 graphics, so you'd need a separate graphics card.
Now the reasons for going with the older designs with DDR3 memory is if you already have a lot of existing DDR3 RAM in your existing computer system, so you could reuse those. This is not a bad idea, as currently there is a huge shortage of DDR4 RAM, and their cost is well beyond reasonable. So if you can keep using your existing DDR3, then you should do so. The reason not to do this is that there will be no further development on this line, and no further upgrade paths. Next-next upgrade will require dumping the DDR3 and the motherboard and processor anyways, but these days people are easily getting upto 5 years from their rigs, so it may not be an issue for years.
If you're ready to upgrade to DDR4, then you should get the two designs that use the modern AM4 motherboards with DDR4. As mentioned DDR4 is unreasonably expensive now. Another thing that's unreasonably expensive right now are graphics cards, due to the Bitcoin and other cryptocurrency mining craze. So for that reason, you would probably do well to get the A10 processor because it has the embedded R7 graphics, that way you save on at least buying of a new graphics card for the moment.
However, I would suggest that you skip all of these, and get yourself either a Ryzen 3 2200G or Ryzen 5 2400G, which are two processors with embedded graphics. Their graphics is much better than the R7 graphics, as they use the newer generation RX Vega graphics. And of course, their CPU performance is much better than the old-school Bulldozer CPU's. They will both use the same AM4 motherboard with DDR4 RAM too.