In the beginning, try a nation that has simple magic. As an example, Man has Nature and Air, and not much else.
Nature magic:
Nature has some interesting summon (Conjuration) spells. Vinemen are cheap, and Vine Ogres almost as viable. To achieve Nature 3 of the Vine Ogres, you will want a booster. Construction 4 allows any of your Nature 2 mages to build Thistle Mace, which gives them +1 Nature magic. Construction 2 allows you to build Vine Crown, which makes both summons more effective.
Summon Animals is quite expensive, and the animals aren't very good in battle. However, if your capital is forest, mountain and/or swamp, you have better chance of getting something useful. (Press 'i' to check province information).
Nature isn't very offensive path. It has good support spells though: e.g. Eagle Eyes at Alteration 1, Personal Regeneration and then Regeneration at Enchantment, and Relief at Enchantment 6. The few Nature spells that can be used offensively aren't very good besides Charm, which can sometimes get you even mages!
Air magic:
Air, on the other hand, is very offensive. All offensive Air spell go right through armor. This could kill your own units as well, if Air magic didn't increase the casting mage's precision and allow you to cast Aim. Sometimes the mages cast Aim at archers instead of themselves or fellow mages, which isn't nearly as ueful.

With Air, you should go for Evocation. Lightning Bolt is probably enough for you.
As for items, Flying Boots are very useful. Air boosters are hard to get to, but once you get one, you can build another as well. Bag of Winds and Winged Helmet need Air 3, which means a lucky Crone or your pretender.
If you go for stealthy forces, you can use Conjuration spell Call of the Wild and Call of the Winds to drop Werewolf and his pack wolves or a pretty useless flock of Black Hawks to a province. Wolves are stealthy, and Hawks might be able to catch enemy mages, or at least slow down archers. They attack in magic phase, before normal movement or battles, though.
Military:
As Man, Longbowmen are your most powerful national units. Use them with a screen of shielded troops to hold back the enemy (Hold&Attack) while your longbowmen are firing at them (2 groups set at Fire Closest and Fire Archer, or Fire Closest and Fire -). Try to find out how far bacl the Longbowmen can be set, that gives you many more turns of deadly arrows.
When you start to have money and resources and want to do special forces, you can go for Stealth:
Wardens of Avalon are stealthy, Monks are stealthy and can bless them, Druids are stealthy and can keep their morale up AND, as spies, Bards can tell you of the enemy defences; in addition, one of your mages is stealthy. If you find province defended by a Druid, you can recruit stealthy archers as well.
You could also go for Knights. Your Knights of Avalon are very powerful, because they heal their battle wounds (rejuvenation). This allows them to collect lots of experience without becoming too weakened. You can have small groups quite early, and use them to attack e.g. enemy archers. However, don't overdo it - a lone knight will die, and if you recruit them too early, you can't afford mages and archers.
Sample build:
You could take e.g. a Phoenix with Fire 4, Air 6, an 80-point Castle, Dominion 5 and e.g. 1 pick in Order, Production, Growth and Magic. This would give you bonus in research, extra money and resource, access to Air boosters once you research construction, and early spell support. Air 6 gives your Wardens weak Air Shield, Fire 4 gives them +2 attack.
Early game:
Buy Mothers of Avalon, with one Crone if you have the money. Research Evocation 1. This gets your Phoenix few useful spells.
Early on, just recruit Longbowmen. Avoid provinces that have crossbowmen, knights, longbowmen or heavy cavalry. Try to attack provinces under your dominion; if your Phoenix dies in positive dominion, his Immortality saves him.
Send a Mother to search all forest, waste, swamp and mountain provinces. Pay attention to scales. If a province has Death scale, it probably has a Death site. Forests have more Nature and Air sites. Mountains and Wastes also have more sites than plains. Farmlands have only few sites. If a Mother doesn't find any sites in Mountain or Waste, search with your pretender. If no sites are found in Forest, Waste, Mountain or Swamp, search with Crone or with Thaumaturgy 2 Auspex and Haruspex.
More on magic:
First, lets go for Evocation. 1 gives him Fire Darts and Fire Bold; just have him Cast Spells. 2 gives him Flare and Sulphur Haze. They are good spells, but more useful for Fire 6 Air 4 than Fire 4 Air 6 Phoenix. Evoc. 2 also has Vine Arrow for your mages, and Lightning Bolt. Evoc.
3 would have Fireball and 4 Thunder Strike, which are more useful for this Phoenix, but Evoc. 2 is fine in the beginning.
After Evoc. 2, research Conjuration 3. Recruit a Daughter to summon Vinemen (use 'm', monthly ritual) if you have found any nature sites or have conquered Forest provinces. After 2 you can Summon Animals, but remember that different animals come in different terrain. Conjuration 3 gives your Phoenix Phoenix Power, +1 Fire magic for the end of the battle. It allows him to cast more Fire spells before fatique makes him unconscious (at 100).
You could also summon Vine Ogres, but don't. They are good, but not worth summoning with a Crone. Instead, research Construction. At 2, make your Vineman-summoning Daughter a Vine Crown. At 4, give her a Thistle Mace and change her to summon Vine Ogres.
They you can go for higher Evocation, then maybe for more Construction, or Thaumaturgy 2 (search for sites without leaving a lab!) or Conjuration (Maggots, Howl, Lamias, Lamia Queens).