I'll have much more thorough information on equipment, especially arms and armor, in that section. For now, this is just some thoughts on equipment in general and its usefulness (or lack thereof).
Weapons: For reasons I've already gone over, I'm a big fan of short-bladed weapons because of the speed factor. All bladed weapons (short, long, one-handed, two-handed, whatever) are now covered under the same skill. Because of this and the encumberance issue, I believe my original argument is stronger, though I am sure there are many who would disagree. Anyway, my advice is to carry and use the weapon that you believe provides the biggest bang for the buck (speed and damage when weighed against encumberance). And keep it repaired. Worn weapons do less damage than weapons in good condition and worn armor provides less protection. So keep that stuff repaired.
Armor: Essentially the same argument as with the weapons. I have traditionally preferred light armors, but mainly because of the weight issue (less armor means more room for loot). The devs have tried to deal with this in a constructive way, though, because when you hit Expert in Heavy Armor, you lose half of the encumberance (no encumberance for an Expert in Light Armor) and when you hit Master in Heavy Armor, you lose all of it. Which means all of you tank-types can collect and use that full set of Daedric armor and still have room for jello. For both Light and Heavy Armor, when you hit Journeyman, your armor will degrade at half the normal rate, which means fewer trips to the repair shop.
Repair Hammers: highly recommended that you carry 5 to 10 hammers when you head out into the great unknown (more if you are still a Novice in Armorer). Although you can probably replace non-enchanted weapons rather than repair them, if you work your Armorer skill up to Journeyman, you can repair enchanted items, too. Although there is a weight issue (each hammer weighs a pound), a Master Armorer only needs one hammer. And since Armorer helps you raise your Endurance, which means more Health points at level-up, it's well worth the effort.
On the subject of repairing items, even though you can't repair enchanted items yourself, you can take them to any smith or armorer and pay to have them repaired. As a general rule of thumb, it's only a septim or so for each point below 100%, times the quality of the material (repairing Iron or Steel is cheap, repairing Ebony or Daedric really costs). Repairing an enchanted weapon will not restore the charges on that item, though. You'll either need to do that yourself by filling and using Soul Gems or the occasional Varla Stone from Ayleid ruins, or by taking it to one of the Mages Guildhalls and having the resident enchanter do it for you. Doing it yourself is much cheaper (I was about to say "and good for the old Enchant skill," but that's Morrowind - brain fart).
Torches: a nice change for the better - no weight. However, it's also a trade-off because you cannot use a torch at the same time that you are using a shield or if you are using a two-handed weapon. Torches are also a no-no for sneaky-types because they increase your chances of being detected. Better to use Night-Eye spells or potions. Eventually you're going to find a ring or an amulet that has a constant-effect Night-Eye or you'll possibly be able to make one with one of the Sigil Stones that you get from closing Oblivion Gates, at which point you can forget the whole torch-thing anyway.
Lockpicks: they break frequently and are always in short supply. This is probably the best reason to develop your Alteration skill. Of course, when you hit Master in Security, you'll be breaking fewer picks because none of your pins will drop, but it still seems like I'm always running short on lockpicks. Fortunately they, too, have no weight. You can find them almost anywhere as levelled loot, Bandits and Goblins usually have some, merchants occasionally have a couple and members of the Thieves Guild can purchase them from any fence.
Clothing: generally useless, except to sell or to Enchant. Since the Unarmored skill went away, there doesn't seem to be any reason to keep it around. I'm sure that there must be a practical reason for its relative abundance (aside from the enchanted stuff, of course, and the obvious Barbie-doll effect), but until I can figure out what that reason is, it's junk. Aside from hoods, did anyone else notice that there is no non-armor headwear? OK, after giving some thought to the matter, I think I may have come up with a good reason for clothing: weight. Although it doesn't provide armor protection (but it counts as Light Armor for skill purposes - go figure), it's light enough that you can carry a lot of it, it's worth a lot more after it has been enchanted and it doesn't need to be repaired or recharged.
Enchanted items: way cool and way useful (sometimes). About the time that you level into the teens, you're going to start finding a lot of enchanted items. This is especially true on the other side of the Oblivion gates where it seems that every Dremora is a walking magic shop (perhaps that's a side benefits of raising that Luck attribute rather than a reflection of the way things actually are). The numerical limits are two rings, one amulet, and one piece each of the armor or clothing covering that body part (you can't wear enchanted armor boots and enchanted shoes at the same time, for example). Weapons are a cast-on-strike sort of thing, while armor, clothing and jewelry items are constant-effect.
Enchanted weapons have effects that are released when you smack a creature with that weapon. Because of this, you'll need to recharge your weapons as those charges are drained off and the way to do that is to either Soul Trap critters before you kill them, use filled Soul Gems that you pick up as loot or find laying around the Mages Guildhalls (those are generally freebies if you've joined, by the way) or take them to an Enchanter.
If you're going to Soul Trap, you'll need to have a suitable soul gem in your inventory when you do it. Unlike Morrowind, which started with the largest available soul gem and worked its way down (how many of us have ground our teeth in frustration at finding a Mud Crab or a Rat inside a Grand Soul gem?), Oblivion starts at the smallest available soul gem and works its way up until it finds one of suitable size. If there isn't a suitable one in your inventory, the spell simply fails and you'll get a message to that effect.
On the subject of soul gems, I stumbled across an exploit in the game that will give you infinite soul gems of any kind. All you need are at least three of each kind (Petty, Lesser, Common, Greater, Grand and Black), filled with the appropriate kind of soul (Petty in Petty, Greater in Greater, NPCs in Black, etc.). Now go find any container (even dead bodies will work for this) and put all of those soul gems into the container. They should stack together, so where you had 18 filled soul gems, you should now have six stacks of three. Take those stacks out into your inventory and you're done. The next time that you try to Soul Trap something, the game will create an appropriate soul gem in your inventory for you (you folks who like to use Umbra are probably going w00t-w00t about now). The only limitation on this is that it will only create a number of soul gems that is one less than the stack that you have in your inventory. So you'll have to periodically restack them. To do this, put the individual soul gems into the container first and then move the stack into the container. If you move the stack first, the individual ones will disappear from your inventory and you're back to where you started. There is a weight issue to consider with this, but you can always split the stack by moving most of them into a container in your house or selling off the excess.