why would you take spellthiefs edge, every time you cs it stops giving you gold. And it depends on your matchup, if you want to be spamming spells and think you might go oom start a dorans ring, if its someone annoying and bursty like zed, kha'zix, lee sin, or riven start dorans shield, and if its someone you want to be aggressive against start dorans blade (eg. yasuo, singed, some other crazy nonsense champ)

Boots if you're facing someone like Darius or Garen.

Accidentally clicked dorans blade. When i play Teeto (i'm starting to for ta lols), i go double doran ring, and build a liandry's first.

Spellthief edge disables when you try to get cs.
Doran's Blade is not really good on a teemo (cuz teemo uses AP)
Doran's Shield is only if you are expecting alot of harass.
Doran's ring is a viable choice.

Doran's Ring is probably the best start. Doran's Blade isn't that great on him, other than a little with last-hitting (about 3 damage, Toxic Shot already has on-hit damage scaling from AP). The AP from Doran's Ring will out-damage the AD from the Blade, from your Toxic Shot (and Blind Shot). Spellthief's Edge isn't that great on a laner, as you won't really be making use of the pickpocket passive that well. It's actually less mana regeneration (as you do not get mana per kill), so I would definitely advise against it if you are taking 2 Health/1 Mana Potion with it. The 2 Gold per/10 gives about 100 gold at the 10 minute mark, while Doran's Ring is already very gold-efficient (extra health, AP, mana per kill).

Teemo isn't really suited for mid lane, as he relies on autoattack harassing, and he already gets out-ranged by most champions that go there. It's also much easier to draw creep aggression, which will make the trade more likely to be in the enemy's favour. Although he's not really a good pick at all, if you want to play him, I'd recommend you go top with him. Most of the champions there will likely be melee, being very easy to harass.

Forgot to include an explanation for Doran's Shield, but I guess it's fairly obvious anyways. It's an incredibly great item, but not really for Teemo. Nobody would really want to trade autos with you if they're ranged (unless they massively outrange you, like Annie), as you'd almost always win. Melee champions would probably win/do about the same to you, but the strength of Teemo's harass is that [i]he is ranged[/i]. If they can't go in your face, then Doran's Shield is relatively useless. Not to mention that you have your Blind Shot (if they do get in range), which makes the damage reduction on Doran's Shield completly useless during its effect.