Vayne is a very mobile single target AD Carry. Unlike other AD carries, Vayne's single target DPS is very high starting from level one. Abusing this advantage in the laning phase will lead to a strong snowball. Vayne's great strength lies in her mobility, Tumble is easily one of the best mobility skills ever put on an AD carry, using it effectively with her passive makes escaping Vayne nearly impossible.

Pros
Excellent Farmer
Awesome Escape mechanism
Insanly high damage
Really fun to play


Cons
Squishy
Squishy
Even more squishy
Hard to play

Boots of speed health potion3 is necessary if you're laning with a non-sustain support such as Blitz, Leona or Janna. Boot3x has become extremely popular recently due to it's high mobility, which opens up a lot of defensive/aggressive options in the laning phase. It's honestly a breath of fresh air compared to the stagnant/farming Dorans v Dorans matchup.

Pro: More skill based, can out-play enemies that run Dorans.
Con: Can die very easily to level 2 jungle ganks. You spend 105G on pots.

dorans-blade Doran's is still good as hell, if you have a sustain support, then be my guest. Dorans still offer great pushing/trading potential, also easier last hitting, which is always good.

Pro: Very tanky vs ganks, can push very fast, can trade hit for hit.
Con: Not very mobile, can only really capitalize on "mistakes" instead of out playing.