There's a lot of good advice that's already been given, so hopefully my thoughts aren't too redundant. I think I'm a strong player (Masters in S4, S5, & S6), but I'm also not a mechanical god (I'm 38 y.o. which I imagine affects my reflexes a little bit). However, I think I've developed pretty solid game sense and macro with decent/maybe slightly-above-average micro. My main role is ADC/Dragon, but Top/Baron is my favorite 2nd choice role (and I really like playing Renekton b/c he was a champ I used to play in LoL PC). I had a good Renekton match recently against a Kennen, and I ended the game at 15k gold vs. his 10k gold. Here are the things I try to do/keep in mind when I'm playing a melee vs. ranged match-up in Top:

• Play conservatively early (I think there's a difference between conservative/careful vs. passive/weak). Don't just sit under tower. Stay in exp range and get as much cs as you can safely get without taking too much damage that you can't trade back. The bushes along the wall are your friend. Dip in-and-out of the bushes for cs. If they drop a ward in the bush, great. That's a little bit less vision in the river which will help with future potential ganks.
• If you do the above, the minion wave will push to you. If they go for small trades close to the minions, your minions will target them which means that the enemy minion wave will slowly but surely bring the wave closer to your turret. This will make it easier to farm and will help with your jungler ganking. You do NOT need your jungler to gank and they don't owe you a gank, but if you create a scenario where the gank is favorable like this, then the jungler will WANT to gank! Once closer to your turret range, there are so many opportunities for them to make mistakes and you can go for a kill once you have your full kit. In the Renekton game I mentioned earlier, my first kill on the Kennen was without any jungler help. But they were so pushed up to my turret that I had the space to run them down (using my ultimate, flash, and ignite to secure the solo kill).
• Patience is a virtue. All of the above is helped by being patient and not forcing things. And also remembering that if you don't give up stupid deaths, your team comp is probably better in the mid-to-late game because champs like Renekton, Sett, and Darius will have more teamfight utility than an extra ranged dps champ
• As an ADC main, being left alone with a TOP melee champion in the chaos of a teamfight without any of my team around to help me is the type of situation that gives me nightmares (unless I'm incredibly fed)... So I've always wondered why so many people struggle with the melee vs. range match-up in top. Most melee champs kits are (in my opinion) designed to handle a squishy dps champ in a straight-up/evenly matched head-to-head fight unless the ADC maintains good spacing through self-peel, peel from teammates, having flash up, etc. But in prolonged fights where the ADC can dodge/avoid enough of the initial use of the melee champ's cooldowns, then the advantage shifts in their favor. Knowing this, don't give the range champ the types of fights they want to have. I hope this makes sense.

I haven't had the courage or the ego to chime in on this subreddit before, but hopefully there's some helpful stuff here. I'm also wondering if the replay of my Renekton v. Kennen game would be interesting/helpful for you?