Well, considering that I'm biased in this (having written one of those mods), I can't give you a straight answer. At least not in good faith. However, I can try to answer specific parts of your question.

Balancing is a very subjective topic. We all addressed it differently (just take a look at the weapons in each mod), though there may be some overlap in certain areas (like the farms, for example). I can't say which one is better in that regard.

As for general bugfixes, Autumn Twilight probably has the most. At least I tried to fix as many as I could. APT 1 and 2 are the next-best, followed by Tolmekian's and MarvinKosh's mods.

Regarding AI-bugs, there are two kinds of those:

1. Bugs in the AI-code itself.
2. Bugs in other parts of the game, that affect the AI-performance.

Nr. 1 can't be fixed by us modders, because the AI is hardcoded, and we don't have access to the source-code. However, because there isn't just one AI in the game, but several AI Personalities, we can work around this. We simply replaced the AI Personalities of the afflicted races with working ones. The actual AIP used is different in each mod. For example, Tolmekian uses AIP 11 for all races, while MarvinKosh uses AIP 8. Using only one AIP for all races makes it easier to address the issues from Nr. 2, but it also makes all the races play the same. Due to this, I decided to keep the different AIPs for all the races, and only replace the one that is truly broken, AIP 10.

Nr. 2 are, for example, mis-cagetorised techs, causing the AI to ignore them; certain techs and planetary improvements having been assigned a too high (or low) value, causing the AI to over- (or under-) value them; too many starbase modules in the game, causing the AI to be unable to use several of them (the AI can only use the first 100 in the file), etc. Those are things we modders can fix. Overall, I'd say, that the mods are pretty even in this area. The only exception is APT 1. Some of those bugs would require balancing-changes in order to fix them, which is outside of the scope of this mod.

All of the mods are perfectly playable. There are some big and small changes in each of them, but you should have no problem to quickly adjust to them. The only exception is MarvinKosh's mod. That one may be a little difficult to get into at first, because it is very different from the regular game. The tech trees alone have been completely restructured and are, due to the way the UI works, a bit hard to navigate. In my opinion, APT 1 is probably the best in this category, because it is primarily a bugfix, with only minimal changes to the game.

As for keeping the game as close to the regular version, I'd say APT 1 is the best in this area too, for the same reasons as above. I tried to stay as close to the regular game in Autumn Twilight as I could, but the way I fixed some of the bugs, and several of my balance-changes, make it feel quite different in certain areas. The same can be said about Tolmekian's mod. APT 2 is much closer to Dark Avatar (the first expansion) than Twilight of the Arnor. It also contains several changes to the UI. MarvinKosh's mod, as already mentioned, is very different from the base game. Along with the tech tree changes, research is much slower, and you only start with a few Super Projects, to give some examples.

Well, I hope that was helpful for you.

I would also recommend starting with APT1. It's pretty much what I did with my own personal fix mod; some of the others are quite different from the vanilla game and don't interest me that much. In my view you should at least play the game as it was meant to be played before deciding how you want to change it.