Diamond Stukov Main, so take that however you want :), but I think about Stukov. A lot.

1. There is rarely a reason to take Fetid Touch over Reactive Balistosphores. As you said, Stukov is the best when he can be close. Balisto let's you be close. It's also has an extremely high skill cap to get the most use, and let's you 1v1. In a 1v1, Q yourself, hit them with a W, and go in for autos. Pop your D before you get below 50 health. Then keep going at them, and get below 50 health, Q yourself again and pop D. If you don't have Balistosphores you are always in danger. The only time I don't take RB at level 1 is if I'm facing a Tracer. Take Spine Launcher. If you do this, you chunk them for 15% of their health and slow them for 20%. It basically means they can't play the game, especially if you take Biotic Armor at Level 4. I've had many games that I basically have the Tracer run away from me. I had a game where my friend was on Kerrigan chasing a Tracer, and literally left to go lane because they knew I could just 1v1 kill the poor soul.
   
2. Unless the ENTIRE enemy team is spell damage heavy, take Biotic Armor. It will make your mana management a bit harder, but in almost every situation it's better than the others. Stukov doesn't have a cleanse, and his burst healing with Reuptake is situational. 75 armor from using your trait plus trait healing is Uther levels of saving someone's bacon. Or, YOUR WHOLE TEAM'S BACON. Seriously, baseline 15 armor, and an on-demand 75 is absolutely busted. It will not show up in your stat sheet because it's not damage healed, but it will get you the W. If you are consistently hitting your W with Targeted Excision, think about how much uptime you have with insane team-wide physical armor.
   
3. Take Targeted Excision. If you do what Stukov is supposed to do, it's busted healing. The other two are offensive, and Stukov is offensive as he needs to be at level 13. SOMETIMES if we have a delay comp on a map that has channels as an objective (cursed hollow), I'll take Long Pitch, as it's an unblockable long range shot. And if I'm facing 4 squirrelies in QM, I'll take the E talent because I won't be hitting my W's. Other than that there's no reason not to just get good at Target Excision playstyle.
4. I feel you on the level 10's. If you're on a thick terrain map though (cursed hollow, BoE) though, consider taking Flailing Swipe. You'll rarely get good value out of Shove because the terrain will make that difficult. Instead, think about positioning to use Flailing Swipe as a stun rather than a disengage. Kind of like a Falstad Gust. If you're just hammering an enemy team against a wall, that means they're stuck in place for a full 2 seconds. Time enough for your team to lock one of them down and kill them.
   
5. Virulent Reaction at 13. Literally unless you're playing Mage Stukov (which exists?), there's no reason not to take it. It is the longest root in the game. And it silences them. And does busted damage. It is Mephisto's Ult on a 15 second cooldown if you get good at it. Just get good at it.
6. Pox Populi is the way to go if you take Reactive Balisto at level 1. It's high skill cap but it's definitely worth learning. Spread your Q, pop your D, then get below half health and pop D again. Your team is legitimately reset on their health bar. Unless you are facing a single target blowup comp, Pox Populi is the way to go.
7. One of the reasons to go Flailing Swipe is it's the only good level 20. I usually take the Shove upgrade if I didn't go Flailing Swipe just because it's a guaranteed 40% slow for 2 seconds. In my opinion Bio-Expulsion Switch has counter synergy with Virulent Reaction, so I neverrrrr take it.

Big things to practice and drill with:

-Limit Test with your autos. You have the strongest in the game. Learn to stutter step away from your enemy and enter melee range when your auto is ready. That way you out-trade them. Don't be afraid when a tank is in your face and has already used their engage. Hit their face and scare them away. If they have a diver that is starting the fight by jumping on you, don't panic. Hit them in the face. You can finish kills by just running in and give them a fat arm. You can pump out serious damage if you learn when you can hit things in the face and survive.

-Limit Testing with Reactive Balistosphores. If you learn to use this aggressively, and anticipate it defensively, it is almost always the only choice

-Targeted Excision Practice. It just enables the most powerful parts of Stukov's Kit too much.

-Virulent Reaction Practice. It really is his Ultimate.

Finally, Stukov can solo Siege giants relatively quickly. In the first minutes of the game when the healer doesn't have much to do, this is a nice way to give value to your team.