If you're playing against the AI only, putting most everything on automation is okay to do, minus the cap carrier missile platform ability (it tends to drop those the moment it goes into combat mode, leaving them, often, far from the battle).

Against another player, there's not too too many you want to leave on automation unless you have a massive fleet. The Hoshiko's repair ability is good to leave automated, as well as the Dunov's (?) Shield Restore for a TEC player (if you can't tell, I usually play TEC). Most of the special attack abilities are also usually fine to leave on auto-fire, like Flak cannons, Gausse Rail guns on Kols, Radiation missiles, etc. Special support abilities you may want to learn how to set up command keys to quick-select your support vessels so you can quickly get to their abilities to call them up. In the middle of a massive fleet battle it can often be hard to quickly pick out your support vessels so having them quick keyed can be a real boon.

Here's my overall gaming philosophy, modified by SoaSE's specific capabilities and features:

As a poor micromanaging player, I don't play in multiplayer games. I enjoy these games' single-player mode for what they are; only a real challenge to the "casual" player. "Hardcore" players tend to have "unbeatable strats" that they pass around which will allow "anyone" (read: other hardcore number-crunching min/maxers) to beat the single-player AI even at its most brutal settings. This an industry fact that has yet to be gotten around, even with AoE III's brutal and "cheating" AI.

If you feel that you have the potential to be a great micromanaging hardcore player, forget playing single-player mode and immediately jump into multi-player, unless there's no games to be had at the time. Even if it means defeat, play the vets and learn from them.

I know my limitations when it comes to games... I suck and no amount of "study" and "practice" make me much better (not sure if it's just a lack of skill in this area or a mental block of some sort, but whichever...) so I stick to the solo play and just adjust game settings to where I have to work at it a bit. Past that, set most everything to automation and just do what I can. The automation AI is pretty good in SoaSE, unlike most games where it seems relatively unintelligent when it comes to auto-firing abilities.

YMMV depending on what you find in yourself as a gamer vs what you can presently do now as a "new player"...