Reasoning behind build
I started out playing armor pen focused mid lane Varus, which I still enjoy and play. But when I tried to play Varus bot lane I was very disappointed with the standard builds for him, I always felt that I did very little damage and was constantly out of mana. I experimented with several different builds and build paths and this one seemed to work the best. This build feels a lot like playing Kog'Mah but it becomes useful much earlier in the game and has much more utility with the ult. He has decent AP ratios so building some AP does not feel like wasted gold at all. The gunblade seems like a sub-optimal build, but like I said he has decent AP ratios and about a third of the total damage is magic damage, the life steal from this item is too strong to pass up.
Pros / Cons
Has very strong AOE mixed damage.
Very good wave clear.
Isn't extremely weak at any point in the game.
Has strong utility that fits with nearly every team comp with the ult.
late game becomes essentially unkillable unless thy have a strong assassin.
Varus is a flex pick so if you need to early pick it gives very little away.
Damage takes a little bit to get ramped all the way up in a team fight, but the little bit of AP you have with the ult gives a decent amount of burst.
You will not be maxing Q on this build because if you do not build mana or armor pen it will just drain you of all of your mana and not be super impactful. Mainly use your abilities to proc the stacks from your W.