I'm 120-113 atm, I don't want to end up playing ranked too soon where I get stuck in low bronze forever because I sucked, but I don't know how many games it will take me to get a lot of the mechanics down better.
It varies by person. Pay attention to who you are matched up with in normals, if you start seeing a lot of folks with silver or gold borders, it means you are almost certainly ready to start ranked. Alternatively, just wait until you feel proficient in each role, you generally want at least three champs, a main, someone who counters your main's counters, and a backup in case your main gets picked or banned. Also, you generally want 3/4 complete rune pages, an AD page, an AP page, and a jungle page. A support page is nice, but often the AD/AP pages are usable if you lack IP.
Not how many normals, you can play lots of normals and still be bad. Have at least 5 champions for each role and be decent at them and have rune pages too for ad and ap at least. After that play a co op Ai game or normal with a pro friend and see if you r good enough for most roles.
... And the nugget was like 'PO...TA...TO' and I was all like 'NO, Dude just NO!' IGN: 3Radication