I primarily play top and support and I want to know the community's opinion on which champions can do their jobs with a minimal amount of input from the player. I don't need flashy combos or sick jukes. I just want to win the game by doing the least amount of button presses possible. Any suggestions?
Tahm for both.
Has tankiness, simple minded, nothing flashy, but wins pretty easy.
Top 
Support 
Tahm kench.
no further discussion needed.
top:
support:
(for lulu the important ones are point-click)
Tahm Kench for both, but honestly I think Blitzcrank is a lazier support, and outright the laziest. All you have to do as Blitz is land your hook, and as long as your ADC isn't completely braindead, it's 90% of the time a guaranteed kill.
Hmmmm.
Aurelion Sol, just walk at them right.
But on a more serious note, i would say it really depends on your style. For me the easiest top laners are Illaoi, Camille, And Kled. At least my METE top laners. Illaoi fits my style because i like to go "Fuck it, i ain't gonna sit under this turret and watch the jungler and my laner farm" and ult in there and get a double kill. Shes definitely not the easiest top laner, but shes just how i like a top laner.
As for support, im best at Thresh, Sona, And Tahm Kench. My off metas include Lissandra, Sejuani, and Elise. I like my support (and everyone but top and jng) to be ranged. So i enjoy Thresh a lot. I have only been playing Thresh for about 3 weeks but he fits my style so well I've already got S- twice.
and
Garen/Blitz
Sion is one of the only top laners that can lane into anyone with minimal effort. He isn't stifled nearly as bad as most other tank tops vs ranged champions.
Support = Sona then Janna then Soraka
There are a few honorable mentions like Lulu, but it is easy to mis-click with Lulu if you are putting in minimal effort. Since some of her abilities can target allies, enemies, AND minions. Then you have Alistar and Leona. Both take a little more effort like Lulu since they have skill shots that you can miss.
With , you can't mess up because her heal will always go to the ally with the lowest health with a press of a button. During early laning, you will be on edge a bit if you try to poke a lot. If Sona gets caught early, she insta-dies. That said, Sona would be the easiest support since her only targeted ability is her AoE ult that goes through everything but windwalls and braum shields.
Top:
Support: 
Enchanters aren't best if you're trying to avoid stressful situations as everyone will be trying to kill you.
AP supports are reliant on doing well in lane. They're only a lazy pick if the enemy support is new.
Generally just playing a tank support is sufficient. You don't really need to go above and beyond unless you're playing something like 
and have to be on point with the engage.
Id suggest 
; super tanky, lots of CC, looks like youve got skill when you do well, and has flashy, easily visible contributions
Nautilus is otherwise a very easy, simple champion who is effective as long as you have general tank mechanics down..
