Main Thresh tip would be to think before following a landed Q - you will make your carry unhappy if you bait him in to an awful trade or feed a kill with a bad follow. Other tips would be to practice with your E till you are comfortable with it - it's a fiddly skill that is very powerful when used at its maximum range, especially in combination with Flash (this is your guaranteed set up for your jungler when he ganks - Flash Flay, Lantern if necessary, then Death Sentence/Box once they're slowed). When you're sieging try to hang towards the back (if not searching for a hook) so you can lantern anyone who gets caught to safety. Remember to pick up souls and bring sustain to lane since you don't have any of your own.
Relic Shield is always better than Coin for laning phase, as above - shared regen is amazing since your carry will only come to lane with one potion, and Health >>> Mana Regen for early stats.