NEVER build
. All it does is give a tiny slow to his W. His Q and R already have slows and his E is a suspension, so Rylai's is pretty much completely useless on him. As mentioned above, max W in mid lane for wave control or Q for poke damage. I personally like W because it's easier to farm, and you get no CDR from leveling Q anyway. However, your Q is also a good farming tool. If a unit is killed by it, it refunds 50% of the mana cost. So if you can use it to get three minions that were lined up, you can actually restore mana! Very useful during the laning phase. If you're supporting, defintely max Q though.
As for items, you'll definitely want Morellonomicom first. Gives you a lot of AP, CDR, mana, and grevious wounds. For boots, it's better to take magic pen boots over Ionian and just take some CDR runes. Magic pen is very nice to have. For my second item, I usually take Liandry's Torment. Because the burn passive is doubled against cc'd targets, it should effectively give you about the same power as Ludens while also giving some health and magic pen and being cheaper and easier to get. Deathcap is obviously important for the raw power. After that, I usually take a defensive item if I need one. Zhonyas for AD and ults from
or
. Banshees for AP threats,
ult, or deadly cc such as snares from
or
. Of course if these are REALLY annoying you, then you can get one of these earlier. They're both good items anyway because they give some AP, CDR, and a little bit of armor/magic resist. Luden's Echo isn't really essential so I usually wait to get this as one of my last items, if at all. Still, it's nice for the huge amount of AP it gives and the movement speed is always nice when you're getting chased down so you can kite more easily. If you feel like the game is going well and you feel like you don't need defensive items, then by all means go for Luden's earlier. If the enemy team is building MR, you can also grab a
. It gives you tons of magic pen and a lot of AP. I don't recommend getting any of the hextech items for mid lane . Vel'Koz is an artillery mage, he should be in the back dealing the damage rather than dashing around.
is definitely a good option for support though! Lastly,
looks good on paper, but it's pretty much outclassed by all of the items mentioned above, even with the sheild.
Final build usually looks something like this:
--->
--->
--->
--->
/
---> 
As for your keystone, it kinda depends on what you like. A lot of people take Thunderlords, and I definitely see why. It syncs very well with your passive true damage and it gives you more kill pressure during the laning phase. Personally though, I usually take Deathfire Touch for the late game when there will be more poking and team fighting. I feel like TLD kinda falls off at that point, and I also like the % magic pen from Ferocity rather than the 45% CDR from Cunning( I typically don't need it). Again, pretty much personal preference. TLDR: Thunderlords for early game or Deathfire for late game.
For Summoner spells, you definitely want
. Most champions appreciate the extra mobility for securing kills, escaping, etc. Vel'Koz is no exception, especially considering his lack of mobility. I prefer taking
second. This has saved me from ganks and assassination attempts many times. You can also use it under CC, even when being suppressed by
or
!
is another option for the healing and movement speed, but it won't protect you from an
as well as Barrier. Speaking of Ignite , I wouldn't really recommend it. Although it provides more kill pressure for the laning phase, the range is too short to be very useful for Vel'Koz , who really prefers to be farther away from his opponents.
is one more option if you're dealing with a LOT of CC from the enemy team, but it's rather situational. If you're playing support,
is good as well.
The cool thing about
that sets him apart from many other mages is that even if he's behind, he can still do damage thanks to his passive. Even then, your ult is a giant laser that slows everything in it. If that's not useful, I don't know what is. So even if your lane doesn't go well, stay cool and don't give up!(this applies no matter which champion you're playing, of course)
Well I have more, but it's already been said here by others. Hope I was able to provide some help! And of course it's your choice on how to play, so really you can just take this with a grain of salt if you don't agree. Best of luck out there!