I have Enchant as a minor skill, at 51 points currently (trained). I found a greater soul gem lying around, and decided to give it a try. I'll confess I don't really understand the mechanics of enchanting, even after reading up on it.

Cast soul trap via disposable scroll, and killed an unluck Kagouti that happened to be attacking me. Trapped its soul, and used it on myself.

Only two effects were available; Cure Blight Disease and Cure Common Disease. I don't understand what dictates the available effects, but this is already underwhelming. Cure Common Disease on Self with the weakest effect took up 22 soul points, and only my shield and fancy pants had enough capacity to handle that power. Tried it, and it failed, destroying the soul gem.

My biggest question is, how do you get more available enchantment effects? And other than that, what else am I doing wrong here?

You need to know the spell to be able to enchant it. So if you want to make an enchanted weapon with fire damage, then you need to know a fire damage spell. Also, make sure your item can hold the enchantments. Generally extravagant or better clothes hold stronger enchantments. Also, the strength of the soul you use determines the charge, i'e how many times you can use the enchantment before the cahrge depletes. The more charge, the more times you could cast it.

Also, there are different type of enchanting - Cast on use, cast on strike (best for for weapons, not for bows though) and constant effect. Make sure you selct the right one while enchanting.

More info http://www.uesp.net/wiki/Morrowind:Enchant#General_Tips.

hollaajith pretty much summed it up.

Buy the spells of the enchantments you want to use.

Trap strong creatures in the best possible soul gems to increase your enchantment input power.

Use high quality armor, clothes, accessories and weapons to maintain your enchantment output power.