Theory:
From a philisophical standpoint, and if you want to see it executed, watch most NBA games, though the Lakers are known for it. The idea of the offense is to create great spacing not by great athleticism or screening, but by having a low post threat, and shooters which means that if you don't help on the low block, you will get hurt in post scoring, but if you help, a good post passer will find open shooters who can really fill it up from outside.
Further, there is always the option for a pass to the weak side wing, and because there has not yet been enough time for the cuts to be made, the weak wing can catch and drive essentially to open shooters, or drop for the post player.
In the NBA, the triangle is usually a dominant low post scorer, a dominant guard, and a secondary guard who is still very good. Look at the Bulls during their reign...they had Jordan and Pippen, then one of their white shooters spaced away, they had a serviceable post who could score like Horace Grant, and then they had a stiff white guy who could knock down the 15 footer. Understand that in the NBA LA and Miami are probably the two best examples of the triangle offense, but almost every team runs some sort of triangle principles.
Set Up:
5 to the low block, 3 to the strong side wing, 1 high slightly to the block side, 2 off side wing, and 4 is at the opposite high post, usually just off of the elbow.
Basic Action:
Step 1:
1 passes to the 3, then cuts to the near corner. There is then the initial triangle set. The initial option is for the low post man to get good position, and then seal. (get his defender on his back and create a good post passing angle) The ball can either be directly entered from the 3, or the 3 can pass to the 1 and the ball can be entered in from the corner.
Note: If the ball can not be entered because of backside help, and the post being denied, the post should try to seal his man high, the 4 should pop to the top of the key, and ball should be swung around the perimeter, and attempt to have the 5 release his seal and catch a quick post entry to finish.
Step 2: Once the post is entered, the passer needs to cut through to the opposite side wing position. The cutter can cut off of the 4 in hopes of a quick pass option. The cut's purpose is to prevent a possible double down in the post. Upon the cut, the other players on the perimeter need to fill into stronger post positions. The post is first trying to score, but if he can not, he needs to pass the ball back out to the perimeter.
Sometimes, the opposite post at the elbow will fill to the top of the key, allowing a dive angle for the opposite guard, and allowing the opposite post to have an open shooting position (Basically, every famous Robert Horry shot). The passer cuts past the post to prevent a double down in the post...if the defense would double off the passer, the passer would be wide open on the basket cut. There is the possibility of the 4 man cutting to the high post for a possible high low, while this is done in only certain instances because it does run the risk hurting spacing, or the 4 can set a flare screen for the weakside guard and essentially creating weakside action, and possibility of a skip pass to the guard, of hitting the screener.
Step 3: If the ball is passed back to the perimeter, the ball needs to be reversed to the opposite side of the floor. The 4 would dive down to the block (some coach's might have the 4 screen for the 5, to keep the 5 on the low block, but for the sake of argument, lets assume) and the 5 would cut to the high post. When the ball is then reversed to what was previously the weak wing position, the corner man would cut along the baseline to the opposite corner, creating the same formation, on the opposite side of the floor, creating either a 4-2-1 triangle, or a 4-3-1 triangle, (In triangle, you denote the triangle positions by post-wing-corner...so in a 5-3-1, the 5 would be on the low block, the 3 on the wing, and the 1 in the corner) with the 5 in the opposite high post, the the other perimeter player in the weak wing spot.
Meaning for WIS:
You need at least one post player with high LP. A key part of the triangle is a low post player, and one of the more consistant scoring options. It would help agreat deal if he is a good passer as well, though if you are a lower level school, I would go for LP first. PE for wings is very necessary since it is an offense where because of the inherent spacing of the offense, there are shooting opportunities.
I believe that speed is more imporant that athleticism (you will need both on D, so don't ignore either), but heres why. I have always defined speed as one dimensional movement (a straight line) and athleticism as the ease of three dimensional movement (explosiveness, going around people, creating). Because there is inherent spacing, It is not as difficult to create, simply catch & drive. Athleticism boosts Speed, but I think Speed is far more necessary, since many of the plays in triangle are simple basketball plays.
Your choice of tempo will work either way depending on how skilled you are and how deep you are. My belief is that the game is not going to take terrible shots simply because you speed up the tempo. You may not get as good of a shot as you would simply because you are asking for more possessions, but just because it is uptempo doesn't make it bad. That being said, as would seem intelligent, play the tempo you feel is right for you.
Basically, the triangle is usually determined by 1 post player being very good, and 2 perimeter players no matter the number being good. Personnally, I usually set my PG dist to 1 is because in recruiting, I have found that my best impact pg I have been able to get have a high ath/spd/def, but a near 0 PE, which of course sounds backwards, but if they have the other 2 parts, they can usually drive and kick. If they have high BH & Pass, not to mention the athleticism and speed, they will generally get easy baskets. They won't be jacking up jumpers, but will get some good looks.
In theory, your triangle should be a point guard, a 3 man who can drive and shoot, and a 5 who can really score, and spaced away you have a 2 who can catch & shoot, and 4 who can either dive, post opposite if the pass into the 5 is denied (they would swing the ball around the perimeter until they could enter it into the 4, and then the guards would fill).
I would suppose that as long as one gives at least 3 players within 20% of the distribution of one another, and probably 75% of the overall distribution among those 3 (on the floor at one time...though it could be heavier), the triangle will work. Now, I frankly wouldn't see the problem with giving all 5 players equal distribution if your players were good enough. That would be the best way, because it would make your team the toughest to guard. However, we must opperate under the assumption that you can't recruit 8 studs at one time compared to your competition. Thus, you have to focus your efforts on your 3 or 4 best players, and maybe 1 or 2 key subs.
Basically, the triangle, like motion, flex, the swing etc is a continuity offense. It relies on its own principles to continue running the offense. It is not a set play, but merely a series of cuts and reads which is made.