The AP TEEMO page, this is basically what I would run every game, regardless of my match-up if I would of course be choosing AP Teemo for that match-up.
The ON-HIT VS TANK page, the idea here is to maximize damage against tanks, and the relentless hunter is nice for avoiding engages in instances where you aren't able to harass consistently.
The ON_HIT VS BAD-MATCHUP page, essentially the focus here is to be able to rely on the mallet components to keep you from getting 100-0, and the runes will help you to maintain 100% health, and any time they over-commit and don't manage to kill you, you may be able to heal your way up to actually being able to kill them.
So this is a complicated section as this varies drastically.
First thing is first, your first 4 levels are always the same, they never change no matter your build or your opponent (notes excluded).
Level 1 You never want to start with blind, every champion that it would help against you should probably just avoid fighting at level 1
Level 2 Even if the blind doesn't help the damage will always help with trades, at level 2 EVERYONES auto attacks hurt
Level 3 If you know that you are very unlikely to get ganked, and the move-speed won't help as much as damage in trading, then you can take E again here, but never don't take w at level 4 in that case.
Level 4 No matter the build its imperative to get 2 levels into e to actually deal any damage.
If you are going the ON-HIT build there is only one 'if', if the person relies on auto attacks at all (INCLUDING THE JUNGLER IF YOU ARE GETTING GANKED) , you want to max Q second, if the person does not you can actually gain a cheeky amount of power maxing W second. Either way obviously get R any time you can, and max E first.
If you are going AP build it gets quite complicated, and drastically relies on what items you are building and of course the match-up.
In general you must first decide what to max first:
Try to do this kinda like a flow chart I guess...
Does the person rely on auto attacks for damage?
No - Max E First
If yes then the next question is does the person have a reliable gap closer that you can not avoid easily?
No - Max E First, avoid fights when Q is on cooldown
Yes - Max Q first
Okay, now on what to max second and then in turn third...
Does the utilization of move-quick guarantee your safety against the champion?
No - Max E or Q second
If yes then the next question is does the champion actually have the ability to kill you (in current game state)?
Okay so this obviously has to be broken down to build
My first note is that I recommend starting dorans blade every game, no matter the build or the match-up. The reason being that on one auto attack you are gaining A LOT more from dorans blade than dorans ring, you almost never run out of mana early on teemo, and your starting item should be based on the first few levels... and dorans blade will be better than any other purchase here... always.
Also somewhere in there you want to build Boots as well
With on-hit you are going to go defensive boots, either ninja tabi and
Rest of the build:
Build blade if they are building a health-heavy build that lacks in armor
Build hurricane to maximize your damage and utility in teamfights
Build rage-blade to maximize your damage against a single-target
Build wits-end if your opponent deals magic damage and lacks in magic resistance
Nashors tooth against opponents that you need your q up more often on, also if they lack MR.
There are items that sometimes you will follow up with to other items: Such as if you were to go Wits End/Nashors Tooth and then they build a lot of MR you could get void staff...
If you build Hurricane and everyone on their team builds armor then you can get Black Cleaver
But for the most part these are your items.
You can always pop BVeil or Mecurial Scim if you need to avoid a burst assassin or a long CC effect (Veigar Stun, Morgana Q, Lux Q, similar stuff).
So, 99% of the time I'm going to recommend you rush Sorc boots, first item.
Most of the time Nashors tooth is the correct second item, and this can either be for when you are maxing Q it is great at getting you that 20% CDR fast... or it can be for when you are maxing E and you get that extra attack speed, not to mention the ap damage, and the R/Q cooldown never hurts even if you don't NEED it.
FOLLOW UP ITEMS:
Get this item vs AD assassins, or anyone that is killing you with auto attacks between your blinds.
Get this item if you are very far ahead, or super in the late game, obviously mathematically a solid item
Any High MR Tank that is being bothersome, this helps.
Less of a core item than it used to be, get vs high HP tanks
Very good when you are getting access to the enemy ADC frequently, or if you are winning top vs squish
Pair with Liandrys, enables shrooms to basically carry games, not a good 2nd or even 3rd item usually.
Only get this item after Nashors, and against a VERY high sustain lane opponent, or a soraka support.