coming from a vel'koz main. best thing you can do is probably start the match off with boots against vel'koz. the movement speed will help you dodge his skill shots. champs that i have a hard time dealing with are zed, leblanc, ahri, lux, fizz, akali, and syndra.
however, if your playing a really expeirenced vel'koz player they will more than likely anticipate mobility abilites to get in. so if i was you i would wait and try to bait his E. as its his only move that can save him in a bad situation.
when laning against vel'koz you have to remember that he is one of best true damage dealers in the game. avoid proccing his passive at all costs cuz it hurts like hell. best counter to this is to focus on items that give mr and health. as mr will reduce damage of his abilites while health will somewhat counter his passive as you cant prevent true damage so only more health helps in that situation.
items like
,
,
, and
are essiently useless as most of vel'koz's damage comes from his passive which deals true damage. you can buy them still if you want to reduce his base ability damage to you which will help a little but not alot.