First of all, consider the the two ideas (1) that one should develop weaker pieces first and (2) that the Knights play the role of shock troops in the FIDE-chess army. These two ideas are very closely related.
After 1. e4 e5 2. Nf3 Nc6 3. d4 e:d4 4. N:d4 N:d4? 5. Q:d4, we see the basic "shock troop" idea in miniature. To contest d4, the weak P advances, the two weak Pawns trade each other off, the weak Knights do likewise, and the way is clear for the big pieces to take the field without being harassed by smaller pieces.
After 1. e4 e5 2. Bc1-c3 (not a legal move, but just to set up the example) 3. d4 e:d4 4. B:d4 N:d4 5. Q:d4, White still has the good Queen position, but has given up a Bishop for a Knight. Evidently the Knight is better suited for the shock troop role because it is weaker.
After 1. e4 e5 2. (WA)g1-e3, the WA does not support the advance of the Pawn to d4, and so White cannot use the shock-troop plan. In order to attack/support d4, the WA must either be on d3 (where it blocks the advance d2-d4) or on b2 or f2 (awkward, time-consuming, and weakness-creating). The gambit 1. e4 e5 2. d4 e:d4 3. (WA)b1-d3 is interesting, but because the Colorbound Clobberers use a Queen that does not attack d4, we're not likely to see it in actual play.
Alternatively, 1. e4 e5 2. (FAD)c1-c3 does support the advance to d4, but because the FAD is a strong piece you would not want to play 2...Nc6 3. d4 e:d4 4. (FAD)c3:d4.
After 1. e4 e5 2. (WD)g1-g3, the center is not attacked and d2-d4 is not supported. However, from e3 the WD can support e4-e5 while defending e4, so it can easily be used in shock troop play later on in the game.
After 1. e4 e5 2. (fbNF)b1-c3 Nc6 3. d4 e:d4 4. (fbNF)c3:d4, the fbNF is even stronger on d4 than a N, and for two reasons: (1) the fbNF attacks e5 and c5 instead of f5 and b5; and (2) the fbNF is stronger because it is weaker (because the fbNF is thought to be very slightly weaker than the N, the move 5. (fbNF)d4:c6 can be considered a threat). Of course, 1. e4 e5 2. (fbNF)b1-c3 Nf6 poses different problems!
Finally, 1. e4 e5 2. (fNbB)g1-f3 seems to make no difference, because retreating moves aren't involved.
In the outpost situation, however, all are strong.
For example, after 1. e4 e5 2. d4 d5 3. e:d5 e:d5, the square e5 is a tempting outpost for White. If White occupies e5 with a minor piece, then if Black just leaves it there the piece is very strong, if he trades it off the advanced Pawn may be strong, and if he kicks it out with ...f7-f6 he creates a weakness at e6.
In general, the WD or WA would be the strongest pieces to occupy the outpost e5, because they also attack d5; but the fbNF also defends d4 and attacks f6 and d6, so everything depends on the specific position.
In general, weaker pieces make the best outpost-occupiers because it is harder to kick them out or trade them off, and if they stay on the board, they gain greatly from their outpost positions.
Part of the strength of the outpost is its relationship to your Rooks (although Nimzovich does speak of diagonal outposts). What if you have no Rooks in your army? I have no definite answer to this question, although it sems to me that only part of the strength of an outpost derives from its effect on your Rooks (and on the enemy's Rooks as well).
After 1. d4 d5 2. c4 c6 3. c:d5 c:d5, c5 is an outpost square and e5 is not. Of course, e5 may be a better square because it is more centralized; but c5 is an outpost even if there are no Rooks in the game (remember, the full phrase is "outpost on an open file"), and has the advantage that when you recapture with d4:c5 or b4:c5 you create a menacing potential passed Pawn at c5; but if you recapture with d4:e5 or f4:e5, you get a doubled Pawn.
There are strategical depths to chess with different armies that are as yet unexplored.