The time you should start Pvp is really up to you, but i'd recommend doing it around lv 15-20 to start getting experience against other players. While bots don't challenge you quite as much as players can and will later on, its important that you feel confident in how you play. Getting used to the level of difficulty intermediate bots bring is a good way to help you practice your mechanics and get prepared to deal with other players, with far less stress for failure, and let's be honest here, Less smurfs. Thankfully a lot of smurfs will lose interest after the first level grouping, so by the time you get around level 16 or so, they're less of an issue (Since let's face it, most people who want to pub-stomp, will end up having retarded win-rates by this point and will end up facing other smurfs as a result).
This all said, the most important thing is to be comfortable. Pick a champ you like, test em out in some intermeds, if you like them, or are considering buying them, great! When you feel like you have a good grasp, try out normals! Blind pick is generally easier to get your champion, though by this point you'll see more structured metas popping up, but it shouldn't really be until around level 20 (When tier three runes are accessible) that nitty gritty meta hags should impede your playing a champ for experience.
It is recommended to try out your champion in their native role as much as possible during these learning stages, but its not pivotal, at least not until higher level gates, where your teammates will expect you to provide, or at least attempt providing specific roles. If you're scared of not having a champ for a particular role, grab a 450. They're cheap, mechanically simple, beloved by many, and fairly strong, and can tide the gaps for when you can't play that champ you're dying to learn. Likewise, team builder is a thing now, so if you really want to dedicate to a certain champ and have enough time, you can use that to structure parties.
Once you feel a little more meta-wise (Top,Jungle,Mid,ADC,Support), you can start testing your mettle in draft pick. It lets you ban out all those pesky champs you hate playing, and provides the structure that most upper-level play, and somewhat more importantly Ranked play (If you desire) is centered on.
Last tip
Take your time, especially for ranked once you get to 30. Its better to come into ranked with a solid groundwork, than to rush into the gates looking for skill validation. When you're just starting the game, its fairly easy to overestimate your abilities, or just not be as solid with the framework as you think you are. Having a small cluster of mini-mains to fill other roles is recommendable as getting your role in ranked is not guaranteed, (Solo lanes are highly contested). Likewise if you're a pretty competitive person, ranked is probably going to cause you a lot of stress, as people are much more serious, and its really the cesspool for some of the best and worst aspects of the league community.