First off, if you want to play ADC, I would recommend trying to make a concerted effort to use attack-move. Just hit the "a" key and then click on the target you want to attack. Constantly right-clicking opens you up to much bigger downside risk if you misclick.
With respect to champion selection, the single biggest piece of advice I can give you is to pick a single ADC and stick with them. I don't claim to be the best player in the world, so maybe I am wrong on this, but my feeling is that it will probably be a lot easier to learn the ADC role if you have the same champion every time.
On that note, if you are generally more drawn to casters, then I would focus on playing a caster ADC. Although I personally don't play him, my understanding is that Corki is a very solid caster ADC that you may find more intuitive. Early game, a lot of his power lies in his ability to harass with his q. This might be a skill you are used to from playing midlane casters.
If you want to focus on one of the champions you own, I would tentatively recommend either Sivir or Ashe.
Lucian is a caster ADC, and some might recommend him to you, but a LOT of his power comes from his ability to attack twice after casting any ability, which means that a lot of his power actually comes from auto attacks, with spells just increasing the rate at which he can auto attack. Personally, I think he is a difficult champion to play really well. He is very highly regarded in competitive play, but that doesn't mean he is great to start out with.
Sivir is a champion that seems to be gaining a bit of buzz and momentum in solo queue right now. She has a kit that offers a lot of wave clear potential, but you have to be careful that her abilities don't create chaos in the wave that causes you to miss a lot of CS. Her spell shield is a really powerful ability, but it can be tough to use. Her ult is a team speed up that is insanely powerful and offers great utility, especially mid-game.
Ashe is my favorite ADC personally, so I need to be careful not to be biased one way or another. IMO, she is severely under-rated for solo queue, especially at lower ELOs (although her win rate is actually higher at higher ELOs). That being said, although her w offers decent AoE damage that can help clear waves, she is still very auto attack oriented, especially early. Playing her also typically involves a lot of kiting and positioning. If you are not very comfortable with these types of things, then she may not be the ideal ADC to start with, although I would recommend anyone to give her a try and see how they like her, as I find her to be very fun.
Overall, if you can find a way to try Corki, I think you might find him more to your liking than some of the other ADCs you've tried. Between him and Sivir, I suspect that one of them will allow you to utilize the skill set you've developed mid to jump start your ADC play.
Edit: MF would be another great choice. I admit to not having a lot of knowledge about MF, other than knowing that her win rate in solo queue is very solid. She used to be a premiere lane bully, but I believe that Riot tweaked her to try to make her slightly weaker early and slightly stronger late. Mid-game, her ult is insanely powerful, and if you can hit a good one in a team fight you will almost certainly win the team fight.
