Maintain bush control for chaining barrels.
Take grasp of the undying. Use your Q to apply it with bandit for 10 gold. Don't hurt your mana pool by trying to get SS stacks before you finish triforce + a bf. By that I i mean don't spam Q on minions too badly. Semi-frequently is ok though. Just be patient until you can at least kill the casters with a sheen proc Q.
Always get Fire at Will first. It offers the highest damage increase plus the most reliable one at that. You can decide on the other two at your leisure, but think of it as D. Daughter is better damage and the other one is high utility.
Typically you wanna do triforce, boots, reaver/i.e. (whichever order you want), bt, then a situational item. Reaver is good if you wanna farm a lot, so you'd typically want that first. Bt is usually for if you desperately need the sustain for long drawn out lanes or just staying out to farm longer.
Once you have tri plus a bf you should be able to one shot casters with barrel + Q. Once you have tri + reaver + i.e. you should be able to one shot melee minions plus the casters with the barrel + Q.
Max Q -> E -> R -> W. Always. I can't think of an exception atm.
Avoid people like Fiora and maybe Darius who can harass you easily in early fights. Also avoid ranged laners, or at least try to keep your barrels safe from them. Tanks aren't too rough as long as you can land barrels. That's where chaining from brush works well.
If you ever get ganked, run to your barrels, chain one onto them (it slows them) then run like hell (you get movespeed from detonating barrels). If you want to fight a gank, put an E on yourself and ult on top of yourself. That would probably be your best chance.
Refresh your passive with barrels whenever you can for fights.
Remember barrels cost no mana. Use them as much as you want. They do give 5 gold if destroyed by the enemy laner.
Go 0/12/18 with grasp and bandit. Biscuits are good plus the mana regen for lane. The scaling armor isn't worth on you so take the tenacity mastery plus the healing ones in backet 1 and 3 (I think it's second wind and rejuvenation).
You can do 0/18/12 with thunder lord's if you are super confident, but GOTU is just too good on your Q.
Biggest thing is your gold generation. Just out farm and outscale.
Gl man.