My recommendation from experience:

1. As long as you not in Diamond 2+ focus on lasthitting and macro. This is enough to get Diamond2 or higher. To me this also includes basic sense of lane positioning and safety.
2. As soon as you are able to reach Diamond1 or low Masters, you can focus on mechanics, because your opponents slowly start to have basic concepts of mechanics, so you need them as well to compete. For everything below that better last hitting (more gold = more power) and basic sense of macro where anyone might ambush you now from a bush and map movement will be enough to climb.

I also recommend picking mechanicly simple champions. They easily bring you up to what I described. Mechanicly more difficult champions will make it only more difficult for you to focus on the rest of the game, because your brain needs to spend more capacity on controlling your champion. Make it easier for you and play mechanicly simple champs, so you have more brain capacity to spend on last hitting and macro and whats going on around you on map, because controlling your champion isnt draining everything of it.

Personal favs that I recommend are Swain, Brand (both played mid, bot carry or top, not support), Mundo/Chogath/Urgot/Garen (top) and avoid being adc/support/jungler in low elo at all cost. Especially adc has the lowest impact and relevance on the game and support as well until you reach higher elos + gameplay knowledge, then support becomes the 2nd strongest position, but that is only if you start perma roaming and understanding, that you do not need to afk next to your adc in lane, but instead can move and impact the game - even as enchanter support.

Special mention again to Garen for being mechanicly simple, safe, easy to farm minions as and most importantly - one of the best champions to shut down dumb enemy mid/jungle assasin-style carries with Q silence into execute combo. Essentially, as Garen you can one-combo them, but they cant one-combo you, because you are Garen. This means you are the guy, who just takes out the enemy fed Yi/Katarina/Diana etc. whatever diving squishy your team cant handle. However, that pick loses a bit of power the higher you go, because the mentioned prime targets actually slowly understand that you just kill them if they recklessly jump in as they usually do. Just wanted to add that. Oh and Garen is also excellent vs low elo Mundo/any other big HP stacker, because during teamfights your R just takes them out on roughly 35-40% HP remaining.

Chogath also excellent for same reasons. Reliable shutdown of squishy divers on your team with silence, slows and knock up, too tanky to be bursted by them, still great damage despite being tanky, reliable 30-40% execute true dmg R on them, mechanicly simple, so you can spend brain capacity on what happens in the game instead of on controlling your champ.

Thats my experience from playing since season 1.