Ran it today against Kog'Maw and I basically got raped. It seemed like my shunpo + bouncing blade didn't do as much as his steady autos + nukes. Is there a specific trick to the matchup? And could I get tips on running Kat mid in general?

Also, AP or AD?

AP or AD is like starting a flaming war, it's up to you, really, personally I go AP.

Also Kat mid is nice but kog is OP, the easiest thing to do would be just hold mid, get pots, play safe, and wait for the jungler, or any ally, to gank kog.

Should I have run the fort pot + 5 hp pot build or the doran shield + hp pot one?

Also, I went Q-E-W-E-E-R...would putting priority in Q have been better?

Try to not commit so much just harass with Q and not E

The best way to beat Kat in mid is to not let her kill you. Focus on farming and not dying to her. CALL YOUR MIAs, when Kat won't get a kill on you, she WILL go to other lanes. Ward your side bushes, if you notice Kat's direction when she goes to gank, follow her. Kat is vulnerable for about a 10 second window after she has shupoed in and used her death lotus... unless she gets a kill.

*So wow, that's what I get for posting before I've had my coffee. Read the OP completely backward sorry.

You are doing it wrong man.

Q 1st, you need just 1 point in E.
Every time your Q is up use it, and poke your enemie on mid.

AD works better for me. Cuz Bblade is just much better, and your autoattacks DEAL DMG.

It's not as easy to go against Kog as you think. If you just spam your combo on me I'll pop my w and shoot you 3-4 times as you run away from me. I'll do 2x the damage to you that you did to me.

Best bet is to play defensively and wait for him to overextend w/o creep.

Also, AP > AD all day.

AP = Rylais
Rylais = Utility.

Kat has very little utility as AD. Almost none, in fact.

AP Kat begins contributing sooner and is stronger in the midgame, it adds damage to Shunpo + Ult and once you have Sceptre you get a free snare off your Shunpo.

I find AP Kat to be more viable in all levels of play because I feel personally that her role is to suppress the other team in the early-mid phases when her damage burst is heavy and she can score a lot of kills.

AD Kat will eventually outscale AP Kat but will take longer to get there and will have considerably less defense in the build up.

Core for AP Kat would be Sorcerer's Shoes, Rylai's, Mejai's and either Void Staff or Abyssal Scepter (totalling at ~7800 gold)

For AD Kat, you would likely stack an amount of Bloodthirsters which take longer to build up, don't offer any health/mpen/cdr etc, but will usually out DPS the AP build above.

2 Fully charged Bloodthirsters with shoes is around 7500g and if you can look past the loss in defensive stats and the slow from Rylai's will easily outdamage the AP build with her ult while being a little competitive between BB and Shunpo. Tradeoff is you are weaker until you finish building and charging those BTs and you don't have a reliable slow to kick off your combos.

Against Kog you should harass liberally early on while he still has mana issues and cannot punish you for your repeated attacks. If you wait until you're both level 4-5 to start harassing his punish will cause a lot of problems for you.

Kog is a beast in his current state, and his Barrage skill is highly abusable, even at low ranks.

I've had best success (my usual start, Boots+3HP) by being less aggressive about last hitting, and biding my time for the first several levels. I like to run Exhaust, so if I've kept my HP up until hitting 6, a good KI > Shunpo > BB > Exhaust > Lotus combo will typically be able to kill him, which shifts the balance of power pretty nicely.

Whatever you do, don't die, it will totally ruin your chances to fight him effectively. If he forces you B early, don't just save for your BF, work on your Merc's, as they will keep you in the fight. Also, if the Kog happens to be excessively skilled, or belligerent, or both - call for a gank. A highly aggressive Kog will push hard, so will be easier to gank than a more moderate, wiser Kog, who will simply abuse his insane range to zone you out of harassing him (he's too squishy to zone you out of xp/gold if you play halfway smart yourself).