I'd say the fastest way to climb solo ranked is to pick a high impact hero, and if your team fucks you with their picks be the good guy who repicks into appropriate support or semi-support. I wouldn't recommend carries that require reliable support (Sniper, Drow...) and definitely not junglers other than Chen/Eni/Ench. If your skill is way higher than that of other players then you should use it to win a lane.
I'd recommend good offlaner against weak carries, people don't generally instalock that role so you can go Phoenix/Timber/Nyx/BH/whatever and announce "solo mid or off" and potentially win that lane and/or put a dent in enemy carry while hoping at least one of the other players in mid/safe/jungle are capable of getting good farm with the space you create.