Well, as always, there are no perfect answers to these sorts of questions in Dominions. Style enters, as does people's differing estimations of what is optimal. But here are some tips on the way I like to play Abysia:
First off, the most obvious strength of the race is that the troops are all fire-immune, and many of them have a heat-aura. So fire magic is going to be of interest - you can bLast away without fear of friendly-fire losses. Which is a very good thing, as Abysian mages are notoriously imprecise. Its worth noting that declaring a mage your prophet increases his precision noticeably. So I like to buy an Anathement Dragon on turn 1, and make him my prophet on turn 2. On turn 3, he leads out the 1st army.
Something that I like about Abysia is that the troops don't really require a lot of subtlety
They're all fairly well protected, well armed, and skilled. Just put 'em all in a big mass up front. Place your Anathement prophet somewhat behind them, with a script of Divine Blessing, Flare (which you have pre-researched as Abysia), Smite (because as well as being imprecise Abysian mages are also heavily encumbered, and Flare is a high fatigue spell), Fanaticism, Fanaticism.
I like the Abysian Infantry with morningstars as the core of my armies. They have shields, heat-auras, and deal out good damage. They are also 30 resources apiece, which means they are hard to produce en-masse, so I also buy Humanbred to help make up the numbers. I like the ones with spears. Lava Warriors are wonderful troops, although both gold and resource intensive. I do try to add them to the army mix, and they are the reason I like to have a Divine Blessing in my Anathement's script.
As for a pretender, I personally like the Lord of the Desert Sun. He's fire-immune, comes with both fire and nature magic, and gets free Great Lions at the start of battle. He has fairly high inherent precision, and nature magic allows him to cast Eagle Eyes, boosing that precision up to a really accurate level. I use him as a combat support mage rather than as a supercombattant, but later on he's big enough and has enough skills and item slots that you can turn him into an SC if you feel the need.
Here's how I like to design him: 4 fire (decent bless effect on the Lava Warriors) 3 nature (I'd go higher, but I don't want my sacred mages berserking). 1 order, 2 prod, 3 heat, 3 luck, 1 growth, 1 magic. You can deifinately adjust these scales to taste, but I *enjoy* luck, so I like 3, and I find Abysia needs resources almost more than gold, so prod is higher than order (and order also conflicts with luck).
My 1st research goal is Alteration 1, for Eagle Eyes for my pretender. Once I have it, he joins the main army, set somewhat back and off to the side (to prevent burning up those free lions for as long as possible). He casts Eagle Eyes, Flare, Flare, Flare, Flare.
Your starting scout is an assassin. Don't ignore the possibility of using him to take provinces. If an indie province is left without leaders, all the troops rout if the province is attacked. In fact, I like to spend turn 1 forging a Fire Sword for my assassin. While I'm not sure its worth it, it does seem to give him just that little edge that means he is sucsessful in his first assassination attempts more often than not. So I send him out on turn 2, fire sword in hand, and let him start killing indie commanders in whatever province I think my army would get to Last. Have him keep assassinating until you don't get a message for him - that means he's killed all the commanders, and then you can order him to attack the province, and watch in glee as all the troops run away from your solitary assassin.
I realize I've gone on at some length, and I haven't even gotten into Blood magic, Warloks, and other later-game stuff - maybe next time
Hope this was helpful.