Short Spear

Not quite long enough to scare off cavalry, but might give you a chance not to immediately evaporate under the hooves of anyone out to get you.

Most armies seem to have someone running around with short spears, cheap and cheerful troops for the most part.

Added to a horse archer it gives them that added edge when the charge in for the final kill, and mitigates the effects of shooting and getting caught. Good Value.

Long Spear

Much longer pointy sticks that do a damn fine job of telling cavalry to go elsewhere. Solid in both combat phases, but the power fades as casualties build up.

Reduces the effect of charging lancers and melee experts, so really rather useful.

Getting your TUGs 3 deep massively increases their staying power for a loss of frontage.

Poor Long Spear troops are remarkably resilient, and can really upset people who see them as an easy target.

Mounted Long Spear seems to turn up in the hands of some Arabic cavalry and cataphracts. Cataphracts become really rather good with long spear to remove melee expert or to count against foot spear, all the while having their full armour to keep them going.

Missile Weapons

Power Bow

Terrifying to anything on a horse.
Extra range and ignoring armour means mounted power bow can outshoot anyone else on horse (or camel, or elephant) back.

The nature of movement and charges in MEG means that you will mostly be shooting in the charge phase and may be struggling to get full use of the range, that is until you have shredded the enemy and are moving in for the final kill.

The big issue for power bow is that they are too scary, and no one puts their mounted anywhere near them if they can avoid them, so its difficult for foot to really get a lot of shooting in. And loose order foot are horribly vulnerable to charging lancers. Just don't try and run them down as a 4 of lancers - that will not be pretty.