Ninja Tabi/Merc Treads, BF sword, Vamp scepter, IE, PD, GA/LW/BT.
If you can't stay alive in the teamfight then it's usually your own fault for not using your ult/riposte to keep the heat off of you.
Start boots + pots if it's an easy lane, armour + pots if it's likely you'll need to fight for your supper.
Max Q first if they're vulnerable to harass/can negate your autoattacks. Max W first if they're inclined to leap on you/be aggressive. Max E first in those rare situations where W/Q are inexplicably ineffective.
Ultimately I suspect most Fioras forget that her Q does quite a bit of damage and often allows 4 stacks of her passive (Q->autoattack, then let them get distance and Q->autoattack again), which when combined with Riposte often ensures that you can get in and out dramatically winning the trade by regenerating shortly thereafter. The nice thing about it is that to completely avoid her Q harass they need to avoid the minion wave entirely or spend all their time hiding in brush, both of which eat away at their income. Even if you don't get kills you can deny them enough farm that you have, gold-wise at least, effectively "killed" them several times.
Watch out for Panth, Warwick and Jax. All three are extremely problematic and can wreck her face. Most of the other top laners are a bit easier to deal with. Even Darius and to a lesser extent Teemo can be kicked around if you know what you're doing.
Seriously, she's not that bad. People are just fixated with this hilariously ineffective "tanky DPS" build, or the AoE gimmick that was never necessary nor even particularly viable. When you kit her for single target damage she will effectively instagib most squishies she encounters, and be able to out-fight most bruisers that would thwart her. Just wait for your team to go in, leap on the ADC and kill them before they know what hit them. If they flash, just use your second Q.
Consider taking ignite (great for securing kills, can be cast while ulting) and either flash/ghost as you like. Both have their uses.