Viego mid is viable, but uncommon. You cannot play the same way every game, that is not how this game works. Expect to have a few rough games before you can start feeling out how to play and change your play style. I'll start with what runes to take then talk about what items to build. Good luck and have fun!

(I have a lethality and AP set up for viego. The only thing I want to say about those are to never build them in ranked and only build them with a five stack. They are hilarilous and only for people who know how to play Veigo.)

Conqueror is really good on Viego. He stacks it instantly with standard combo. It gives damage and healing, nothing really compares. However PTA is viable

PTA is not troll. You can run it and have sucess. I would only ever go Press the Attack in a ranged matchup where you want a short trade. This is keystone hsa very specific uses and I would say you just have to feel it out. Not an every game kind of setup, but can work. If you are new, just run Conqueror.

Triumph lets you fight more and gain more health each time you reset your ult. So you get passive heal from possessions + Triumph heal. Alacrity is just the best of the legend runes. Tenacity does nothing because of how little it gives, and bloodline gives stats Viego just doesn't need. Last Stand is good because of how Viego plays, constantly in the middle of teamfights, picking up whoever and dashing in the middle again. Coup de Grace is fine and honestly just preference but I will say that last stand is better for laning.

Bone Plating + Overgrowth lets you fight more. You take less damage in trades, and because it is melee, you farm more, giving you more health, letting you fight longer.

These secondary's are for mage/poke lane. They would pop Bone Plating instantly, so why bother. Revitalize lets your Doran's shield + Second wind keep you topped of during the lane. These are some good runes in general if you don't know what to run second, but there are better ones I will talk about next.

You run Conditioning + Unflinching + Health shard when your lane makes you depressed. Your only option with this lane is to scale and probably just get carried. Never bother fighting, maybe roam, but sit under tower and get the CS you can. Just the most unfun lane, but you have to play like this if you want to play Viego mid.
Another situatoin you talk this in is when you have no idea who you are facing. These do make your laning a bit weaker, but you can past it pretty easily. Unlike in the above situation, this situatation requires you be actually good at the game and out skill your opponent.
In both situations, take TP over ignite. It is more useful for scaling which is exactally what there runes are for.

Here we are, a winning lane. This is a rare treat where you don't need any thing defensive because you run the lane. take Taste of blood because you are the one poking, and Treasure hunter because it rewards you for extending you lead to other lanes. Win your lane, go to others, take over the map, and see the victory screen.

First always rush Blade of the ruined king in lane. I don't actually LOVE bork but it is necessary for laning. It's real power for Viego is in the sustain. It does do a lot of damage but not more than your core damage items.

Next, your core damage itemsBuild these items after BORK in this order: Trinity Force, Kraken Slayer, Black Cleaver. These are you core damage items. Viego stacks Kraken very fast, same with Black Cleaver. Viego also loves having spell blade so lets abuse Triforce while it's strong. The reason we don't go Sunderer is because it is not as good as Triforce. It does less damage, it doesn't give attack speed, its heal is negligible, BUT if they have a bunch of tanks e.g Sion top, Galio mid, Nautilus support then you could build Sunderer. Keep in mind though that you have Blade of the Ruined King, Kraken Slayer, and Black cleaver, that should be enought tank shred.

Last I want to talk about your defensive items. You are building these last. You actually only have one item slot left so choose wisely. Wit's End is Viego's main MR item. With Maw being next to useless and Wit's giving a lot of stats Viego wants. this is a great item. GA is a snowball item. If you are in a game where if you die its over, build this. If you tend to die in someone else's body frequently, don't build this. Instead build Death's Dance. Death's Dance is a good Armor Item for when you aren't ahead. This is probably going to be your last item(At least it should be, all these items should be last), so you may not even finish it, which is fine. If you are building this, you are getting carried, but once you finish it, you will be much stronger.

There may be times where you get a few kills early and have a bunch of gold. If you have 1300 gold, forget Blade of the Ruined King. Buy a Noonquiver and rush Kraken Slayer. Then buy your Triforce and Cleaver. Now you should have two item slots left after boots. Buy two defensive items, usually a Guarduina Angel and either Wit's End if they have a lot of AP, or Sterak's Gage. With two defensive items and your core damage items, they cannot kill you and you do a lot of damage to them. This will not happen every game, but when it does, the enemy fears you. They will flash away from any of your abilities and you get reset upon reset.

Viego is built for jungle, but we want to play him mid. What this means in having to play by ear. Change your runes, think about items, don't turn off your brain. Viego is so much fun and want you to enjoy him. So if you feel like every game is just unplayable, change something. Roam more, play safer, ask for help, change the build around. This is not a hard and fast rule book. This is what I have found that works based on my experience and my observation from high elo players. Someone who mains Veigo mid in challenger in Korea is Need Her. Go find some of his stuff, study it, and take it to heart. This pick requires skill(unlike most midlaner these days) so practice and practice some more. Take over games and have some fun. Go get Isolde back and destroy anyone who gets in the way!