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.