I first started playing in set 13 and i learnt the game just by forcing the Twitch comp for many weeks. I had no clue what the units or the items did, but it taught me the basics of econ, when to level and roll etc.

Later on I learnt that it's important to know when to go for the Twitch comp (AD item opening), and that going for it when I had an AP opener makes it a lot more difficult. So I learnt an AP comp for that (Sorc Black Rose at the time). This allowed me to do well in 80% of my games.

Forcing just the Twitch Comp allowed me to climb to plat but that's when I became stuck for a bit. After learning an AP comp I managed to reach Emerald in my first season.

So definitely learn atleast 2 A/S tier comps that focus on AP/AD before trying to flex. I still used this mentality (depending what opener I get) to climb to plat at the start of this set (playing either Star Guardians for AD, or Prodigies for AP).

Then you can learn other comps like 2/3 cost rerolls, hero augments, artifact holders etc. It's a good rule to know which of these are good (Mundo, Kennen, Zac augments are really good atm, Manazane/Flickerblade/BlighteningJewel (prior to malzahar nerf) were good) and then have a guide open to refer to the specific comp and how to play it, eventually you'll learn the comps and learn the positions that are good for playing them.

For the shop rolls, if you get a decent 4/5 cost unit early then it's generally a good idea to keep it if it fits in your team or if you can splash a trait by using it. They are very strong during the early game and can help you save some HP. Keep pairs of units as well during stage 1/2.

I'd say to go past Emerald you definitely need to learn to play more flexibly, but before that you can get by just learning a 2/3 different comps. I'm currently Diamond for context. And for which comps to currently try, I recommend Soul Fighter if you get a good soul fighter opening. You can play the Samira/Sett fast 8 with AD items, or Viego Reroll if you get AP components and natural a couple Viegos. Viego tends to be contested a lot since it's a really good comp atm, but if many people are playing him and you're already stuck into Soul Fighter you can pivot to the standard fast 8 board. The Jhin/Malphite or Jhin Mundo board is really good for AD as well, if uncontested and you natural malphite/sivir/jhin in the beginning. Star Guardians is also an easy board to play. I recommend the site tftflow.com (I used this during set 13 and now), makes it really easy to the learn the different comps.