It depends, are you more interested in the thinking process or the "best" moves objectively speaking? If you want the best moves, then perhaps a higher rated player (or an engine) may be better to consult than me. If you want reasoning alone ("correct" or not) for analysis, then I'll give it a try 
My first observation is that the position appears roughly equal to me in this "big endgame." White and Black both have 4 minor pieces, both Rooks and 5 pawns each. Maybe Black's pawns are slightly better? I say this because White has 3 pawn islands, while Black would have only 2 with ...b5 "connecting" the two islands (although perhaps not instantly good because a White Rook on the b-file can target that pawn). Another small observation is that White's pieces look slightly more coordinated/active: primarily because the a8 Rook is undeveloped and the c8 Bishop is keeping it locked in, but these things can change. As stands, the position looks fairly equal (maybe a computer can see a small edge somewhere) but I think this is pretty even from a human perspective.
Now we get into the specifics of the pieces:
Since it is White to move, I'll look at this from White's perspective. Probably the biggest thing to jump out is that the c1 Rook and the e3 Bishop are both under attack and both can't be saved. With White's "central pawn chain" on dark squares, the "Bad Bishop" is the dark-squared one, so really, I probably wouldn't mind if Black gave up the f5 Knight for the e3 Bishop. So then where do we move our c1 Rook to save it? Rc2 looks natural to guard a2 and move swiftly on the 2nd rank, but ...Nxe3 forks everything it seems! c2 and f2 Rooks (so we lose material) as well as the g4 "Good Bishop" So Rc2 appears bad for White. Rb1 also looks natural. A sample line may be: 1. Rb1 Nxe3 2. Bxc8 Raxc8 3. Rxb7+ and it looks fairly equal to me. Notice that this feels like a win for White - at least psychologically. Remember that 2 pieces were attacked at the start of this position a few moves ago, so White would be glad to emerge with even material and a fairly equal position.
However, we must think of the words from Emanuel Lasker: "When you see a good move, look for a better one." (Fun fact: this adage is often attributed to Lasker, but the chess quotation was actually circulated prior).
The obvious follow up continuation is then, "what if we don't save the c1 Rook?" Ng2! is an excellent move when you begin to see the details and so I assume this is the one move you mention is "best" (although I don't know what the other close lines you noted would be). I think Ng2! is an exclaim in my mind because in an even material endgame, we sacrifice the exchange. 1. Ng2! Bxc1 2. Bxc1 and White is down in material but I'll come back to this line later. First I want to note how 1. Ng2 Nxe3 2. Nxe3 Bxc1 3. Nd5+! wins on the spot because Black's King can't get near the d5 Knight and the f1 Rook now eyes c1.
Okay, now back to the line I'll call the "mainline." This is 1. Ng2! Bxc1 2. Bxc1 and now we realize how good White's position really is. For instance 2...Ng7 (seeking Bishop trades to activate the a-Rook upon recapture) fails to 3. Rf7+ and picking up the g7 Knight. Here we learn that the "pin" of the f5 Knight is actually significant in this position because Black can't really move this Knight without opening the f-file where a White Rook is already there to pounce. Continuing the "mainline" would probably go 2...Ke8 (or ...Kf8, I am not sure; but it is like Black is practically in zugswang, so we'll just pick some King move). 3. e6 and now the passed pawn on e6 can create some threats while it is defended by the g5 Knight.
Even here though, White's gaining advantage (unless I missed something [which wouldn't be the first time lol]) is only slight and probably still fairly even. Perhaps a higher rated player can pick up where I left off, but I don't think analyzing positions like this to the centipawn really offers much. Without ideas and reasoning, choosing one line a few centipawns "better" than another means nothing if the human player can't understand the "why questions of the position" such as "why not this move?" or "why is that move terrible?" etc.
In the following position there is one main move to make and then two 0.00 moves and a fourth move which is on my stockfish now evaluated at -.16 for white (essentially 0.00). How do you go about finding the top move? White to move. This is from a completed game.