OK, today I'm going to attempt to present my theory as to how the various Apes movies and TV shows fit together.
The first assumption I have to make is that there were several ill-fated flights into deep space that brought humans to the future of an ape-dominated planet. Taylor's ship was the first, followed by Brent's.
Now, on the surface of things, it doesn't make too much sense that Brent was sent to find Taylor, because Taylor's flight was meant to take a long time (hence the suspended animation modules). I don't recall suspended animation mentioned as being part of Brent's ship (it's been too long since seeing "Beneath"), but let's assume that it did, and rather than being sent to find Taylor, Brent and his crew were intended to supplement Taylor's crew in their colonization of a distant world. Never mind the lack of females -- we're talking timelines here!
So, I'm positing that both Taylor and Brent's ship had similar engineering behind them, thus placing them both in the same time period, more or less. Brent's flight left a while after Taylor's, so there was a gap between Taylor and Brent landing in the future.
According to the movie, Taylor left earth in 1972... and I don't recall any specific mention of when Brent left, but given how things progressed in the future before he arrived, I think it's safe to assume that he left earth in 1973.
(Note: In the first movie, Taylor thinks it's 3978, while Brent thinks it's 3955 when he arrives... this is the first time discrepancy in the movies, but if one assumes that the chronometers on the ships were damaged, that's easily explained... there's no reason to believe that either one was right)
Chronologically speaking, the next item of importance would be the arrival of Cornelius, Zira and Milo on present-day earth, using Taylor's ship (or Taylor's ship repaired with parts of Brent's, or vice-versa). This could be interpreted as being 1973 or later. It's entirely possible that Brent's follow-up flight was a top-secret mission, as I don't recall any mention of it.
Hasslein being concerned about what he learned of Earth's future, I'm sure he convinced NASA to send more flights to try to find out what happened, probably intending them to return. This could explain additional missions sent out.
In 1976, Hudson, Carter and Franklin (from the animated series) leave Earth, arriving "over a century" in the future (say, 2080, just for the heck of it), but this could well be wrong.
In 1980, Burke and Virdon's ship leaves earth, and lands in the future (according to their ship's chronometer) in 3085 (a not-unreasonable year, as I'll explain).
Now, I'm convinced that both of those missions were intended to be recon missions of a sort, using different stardrives than Brent or Taylor's ships, which would explain their different arrival times in the future. Since the crews of both ships don't have any memories of Cornelius and Zira arriving in 1973 or so, I would posit that they were under post-hypnotic suggestion to not recall that, but to subconsciously try to gather more detailed information about what's going to happen to cause the apes to take over. (Note: According to Wikpedia, when the ABC-owned stations reran the Apes live-action show as movies, Roddy McDowall reprised his role as an aged Galen, presenting the series as memories of what had happened... and says that Burke and Virdon found a working computer and returned home. This material has never appeared anywhere else, not even on the DVD, but if it's canon, it's entirely possible that by the time they returned to Earth, it was either too late, or the government moved too slowly to take the proper action).
Conquest takes place in 1991. I don't recall when the disease struck that killed the dogs and cats was supposed to have happened, but I would not be at all surprised if the disease was originally developed for other purposes, and was accidentally released, as I've written before.
Battle takes place at the turn of the 21st century, or about 2000 or 2001, depending on how one looks at things. The joint ape-human colony has eschewed technology, but this may have been altered after their encounter with the mutants, who still are using buses, cars, and other vehicles.
Over 600 years later (say, 2600) is when the epilogue of Battle takes place, with peace betwen humans and apes.
Now... 2978 is when Taylor arrived (supposedly), almost 400 years after Battle. Yet, the animated series claims to take place at about 2080, but this can't be right. So, some numbers have to be wrong.
So, let's say instead that the numbers were "fudged" in a few places. The peace between humans and apes would work better around 2200... which still puts Caesar back in history and revered. Heck, even 2100 would work well. And we can assume that the peace lasted for a while, but at some point, someone must have come across some evidence that in the future, apes were supposed to be dominant, with humans as slaves at best. Given that the threats to apes had all been human-caused, it's entirely likely some revolution took place, presumably by gorillas (recall that Cornelius claimed in Escape that it was a gorilla named Aldo who said "no" that sparked the original ape revolution). Possibly around the same time, there could have been an aggressive human underground who felt that the apes were dominating humans anyway, leading to a new ape-human conflict.
Possibly contributing to this would be some re-discovery of technology, embraced by the gorillas (who, as a species, seemed to be more aggressive and violent than they're known by us today... it's entirely possible that, thanks to discovering old movies featuring gorillas as being aggressive, it was taken to heart as to how gorillas should be).
It's possible, then, that within as little as 50 years later (let's say, about 2150), this new ape-human conflict resulted in the future we've seen in Return to the Planet of the Apes. So let's say that instead of "over a century later," as the animated series says, it's really two centuries later, or about 2180 that that series takes place.
But at some point, mechanization and technology was abandoned (possibly because of a rejection of "human technology," although guns remain in use, probably due to the relative ease of manufacture and repair, as well as the effectiveness in killing... most likely, cars and the like were abandoned as remaining fuel reserves were used up and no further sources of oil were available).
By the time of 3080 or so, it's been 900 years since the animated series (this year could be way off, but I'm not trying to fix events into specific years, but rather to put things into an order of some kind). Humans still speak, but don't co-exist with apes entirely peacefully, as slaves are offered up to the apes periodically as a condition of their not being hunted. This is when I figure Burke and Virdon arrive, and their mere presence, with their knowledge of how things used to be, is considered a major threat... even if they successfully returned home, I'm sure that the orangutans and gorillas were convinced that Burke and Virdon may have sparked a revolution of humans, and efforts were made to put the humans in their place.
Raids could have happened on the human villages, forcing them into the wild to fend for themselves. Eventually, the human race could well have reverted into savagery as a result, with no leaders among them (I recall the humans Burke and Virdon encountered tended to be rather meek).
By 3978 (assuming Taylor's chronomenter was right), the Planet of the Apes could easily have been the way it was when Taylor arrived. While there was hope for human and ape co-existence in the past, that ship has sailed.
Now, assuming that all this is correct... why do some characters seem to co-exist in different timelines? There's a Doctor Zaius in the animated series, the live-action tv series, and the first two movies, for example, and there's more than one Urko, and more than one Zira.
Well... it's not unreasonable to assume that some names would occur more than once. "Zaius," "Urko," and "Zira" could be fairly popular ape names among the three species, much like "John" is for us. It's even possible that "Zaius" could even be a title as much as a name. Since none of the movies or tv series delve that much into how ape society works, all we can do is make guesses.
Heck, I'd even think that "Caesar" and "Aldo" would be popular names, given their roles in history, but it's entirely likely that the gorillas revered Aldo so much that nobody even knows of Caesar in the far future.
So far as the presence of a Nova, Brent and Taylor in the animated series... I can't quite explain that.