I'd say there is no reason why you shouldn't just jump right in and play the game, you don't need to read long guides or watch livestreams you won't even understand. Lol has co-op vs ai, which is quite a noob friendly mode where you play against bots, no one will yell at you if you arent very good in there, plus there are tutorials which should help.
As for champions, its worth bearing in mind that one of the ways Riot tried pricing champs was by ease of use, so Ashe and Master Yi who are both 450ip are both easy champs, though that isn't always the case. I'd say the easiest champs by type are: tank - rammus, ranged dps - ashe, melee dps- master yi, mage - annie, support - sona, jungle - nunu.
As for your lack of headset, that's not a problem at all, you will hardly ever see anyone with headsets in solo games.