From a LoL player to another

I would recommend you keep playing a bit more of Blind Draft first. Item build-wise it depends from champion to champion, like if it's a champion that sues AP (ability Power) or AD (Attack Damage). You said you mostly kill with Jax, if I remember correctly he uses AD and AP. For last hitting I guess you should either wait until they are low enough health, at least hit them every now and then to lower the minions health and clear waves faster. Also remember to make your Mastery Pages and Rune Pages (though you should wait for around Lv 20 to get Tier 3 Runes instead). Get used to fighting with and against different champions to have better adaptability and try different roles in case you can't go your favorite role (if you already have done this then that's great). I think that's about al I can say on the matter. Hope you have good luck and lots of fun in your future games.

Heres a tip that took me a long time to figure out, font colors

orange = ad Green = ap White = True damage Yellow = armor Purple = magic resistance

builds are based on a game by game and champ by champ basis but learning the "normal" builds for each champion is a good start. also learning to cs effectively is paramount to a good game. No kills? no problem if you manage to farm correctly. above all else be persistent and have fun :)

If you need to practice CSing, try going making some customs and just practice last hitting with no additional AD. This makes the early game, where CS problems normally occur, easier for you to deal with. As for champions, go with what you're comfortable with. Don't learn to play someone you hate playing as.