Gaimmienne's weapon of choice is the daedric wakazashi, of which she owns several. She keeps extras in her wagon so that when she's away from town for a long time she can keep getting a fresh one when her current one starts to get a dull blade.
As you can see, in her wagon she also keeps a large number of soul gems on hand. You never know when you're going to run into a hoard of Ancient Liches, Dragonlings or Daedric Lords, and you want to be able to trap as many of those powerful souls as possible so that you have plenty for enchanting items.
Every single peice of armor that Gaimmienne wears is enchanted. (You've gotta love that magic item maker at the Mages' Guild.) And most are bound with either the souls of Ancient Liches, Ancient Vampires, or your run-of-the-mill Vampires. Her shield gives her extra spell points and increases her short-blade and dodging skills. Her gloves increase the amount of stuff she can carry, as well as her critical-strike and lock-picking skills. Other peices of armor give her strengthened armor, fortified strength, speed, agility and luck, and almost all of her armor is enchanted with feather-weight (so they each only weigh 0.25 Kg).
Gaimmienne also carries a Water Emerald which lets her breathe and move swiftly under water (the lower levels of those dungeons tend to get flooded). She also has a couple of extra shields, one enchanted with Heal, and the other with Fireball. The Fireball shield is absolutely critical. Gaimmienne is gifted with the spell absorption advantage, and can "recharge" her magicka reserves by shooting herself with the Fireball Shield! She does have to be careful, though. Spell absorption only works when your spell points aren't too high, and if she takes one too many hits from the shield it can do some massive damage. (But then she just has to take a shot or two from the Heal Shield - luckily she's never killed herself by this precarious procedure.)
She also carries some other miscellaneous items, such as a diamond of invisibility and free action (resistance to paralysis). You have to be very careful when there are other spell casters around - if they hit you with a silence spell you can't fight back with your own magicka, and if they get a paralysis spell on you too you're almost as good as dead. That's why she has the diamond. Although, it has been known to not work properly against some of the Liches she's run into. She also has a ring of potent vs. undead and potent vs. humanoid. Her helm of Ghost Form (invisibility and levitation) is nearly worn out, and besides she wants to switch to her new helm (which has a different spell), so she'll probably enchant yet another shield. But of course, the invisibility spell that you can bind to an item is nowhere near as good as the true invisiblity spell which Gaimmienne can cast herself.