Armour

Armour comes down to a choice between light and heavy. Medium armour is entirely useless, since light gives better protection, and weighs less. Also, the best medium armour can cause legal difficulties in Vivec, because Indoril armour is sacred to the ordinators. It has one saving grace - the Ebony Mail artefact, which is the best individual armour piece in the game, but it is hard to get and not worth sacrificing the rest of your AR for. Unarmored is also weak, because its maximum AR is only about 75, and it gives no damage protection, and leaves you with less stuff to enchant when you reach a high level. Two advantages are that you can leave your strength low, and that you can use magic gloves and shoes. This makes it a viable choice for a purely ranged combatant, but not for anybody else.

Heavy armour gives huge protection, and has some very powerful artifacts. If you want sheer power, this is the one, as the Stone Roses sang. However, it is hard to find (a full suit of daedric is only available through selective extermination), and weighs a great deal, leaving little space in your inventory to carry around other items. You need a very high strength to use this effectively.

Light armour gives fairly good protection, and has a couple of great artifacts. It's also very light, allowing you to lug around plenty of loot, and is very easy to obtain, since it can be stolen from a number of easily accessible places, and even bought in Ghostgate.

Some advocate a mix of armour styles, but this makes it harder to increase your skills, and seems fairly pointless, since light is a good balance between weight and protection, and heavy is the greatest 'tank' armour by a long way.

Weapons

I generally take two weapons skills, since most types have different purposes, and are easy to increase. If there are other skills you know you will need, one weapon skill is absolutely fine.

My favorite combination is to take Long Blade as a minor skill and Marksman as a major skill.

-Axe (Strength) Axe has the highest damage potential of any weapon type, but is slow and heavy.
-Blunt Weapon (Strength) Blunt weapons are good for enchanters who want that authentic ‘wizard’s staff’ (knob on end not included) experience. Ebony staves have the highest enchantment capability of any weapon, with a total of ninety points, with a bonemold longbow, the nearest contender, having only forty.
-Hand-to-Hand (Speed) Very easy to increase, because you can keep opponents alive, but fairly feeble as an actual combat skill. Before patch 1.2 it had a tremendous trick which allowed the theft of items from key NPCs who had to be kept alive. Explained in the items section for those with X-Box or an earlier PC version.
-Long Blade (Agility) The best all round weapon type, with the most effective and the most numerous artifacts, good damage, enchantment, and speed. Also easily available in many different varieties.
-Marksman (Agility) Powerful and effective, allows stealth killing and AI glitch killing (see combat FAQ section), and is great for picking off cliff racers. Quite hard to increase though. I would advise for most characters to take this or destruction, so as to have ranged combat capability.
-Short Blade (Agility) Fast and stylish, with good artifacts and readily available weapons. Light enough for thieves, and with some special thief artifacts.
-Spear (Endurance) Very cool, as well as effective. High damage and long reach are let down by speed, weight, difficulty of acquisition, and poor enchantment values. Great artefact available, plus a handy way to increase endurance and get more hit points.