I am playing a swordmage, and have 620 gp. My DM decided to open the shop so that we can buy some items with our cash. I don't know what I can actually use though.
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An abstract answer can be found here in the equipment recommendations. Swordmages, by default, can only use heavy blades as implements. Happily, there are a fair number of heavy blades designed for swordmages. My favourite would be Gith Silver, simply because I like psychic lock. A -2 on top of a -2 from marks for one nasty defender. It keeps you alive longer as well.
Reach extenders are cute, especially with an item set devoted to it (Arcane Bonds) but require specialized builds. Swordmages are hurting for damage, and if you're a melee-focused build IAoP are pretty critical. "Rhythm Blade Wrist Razors (AV2/DSCS, lvl. 3) - This is a very nice way to get the benefit of the Rhythm Blade (+1 AC/Ref) without losing the +3 bonus to AC from your warding."
With 620 gp, you can afford a level 1 or level 2 item. If you don't have a +1 weapon, buy a Magic +1 weapon. If you don't have +1 Armor, buy +1 Armor, and if you don't have +1 neck, buy a +1 neck. Level 2 items are just not that impressive and burning the rest on a couple of healing potions is very much worth it.
If you find yourself doing the defender-dance (prone every other turn) a pair of acrobat boots isn't bad, but only if you have +1 in your 3 primary slots.
To answer the question of the title: Most of them. Just like every other character, you have: head, arms(bracers, since shields break your warding), neck, armor, feet, ring, ring, ki-focus (not used), holy symbol (not used), Tattoo (look at level 3), Boon (kinda not really slotted, but I've never heard of someone having more than one), Waist, and other. There are entirely too many items out there. My personal recommendation is to ask your DM to go to intrinsic bonuses and item rarity, simply to cut down on the stupid numbers of items you'll want to choose from. While this is less critical at low levels, high level item selection is just not fun for anyone (that I've heard).