1000 wins before you ranked.
It usually takes most players about 2000 total matches to be around average skill level, or the entry point for new to ranked accounts in silver 4, baseline 1200 MMR. Assuming you win about 50% of your normal matches its best to try for 1000 wins before venturing into ranked. That way you will probably be about average level and won't get massively stomped and wind up in bronze. This is a game that takes a lot of experience to play well. If this is your first season, and this is your first account, do NOT expect to wind up better than silver something. It takes most players more than 18 months of play time to become a slightly better than average player, or about low gold level.
Take the time to get your experience up. Get your 1000 wins, ask for a Rioter to join you after the 999th. They are fun to play with.
Edit: Having looked at your account and seen your individual skill metrics I would HIGHLY recommend you spend some time improving your skill set before trying any ranked at all. Everything from your builds, to runes and masteries, to your farm rates, and average deaths per game is very sub par. Spend some time watching some streams. Practice on last hitting so you can manage to acquire more than just a mere 25% of the farm available to you. Work on better decision making so you die less frequently. Read some guides and look at some pro builds so you understand where your runes, masteries, and in game item builds are less than ideal. I know it seems like a daunting task, but you will appreciate all the hard work you put in later down the line.
