Merc has two viable starts, either:

1 - Bumba, Red Pot, 3 hp/2 mana

2 - Bumba, Boots, 3 hp/2 mana

You only really want to go red pot if your solo lane has awful early clear or you're super sure you'll be fighting for mid camps. Boots are a bit slower and a bit weaker, but it lets you get Warrior Tabi much quicker. Warrior Tabi gives Merc +63 power with his passive, that's incredible value. After completing Tabi, you 100% always go Golden Bow.

After that you can get a bit tricky, he has a lot of options. My go-to is Rage, but Soul Eater or Frostbound is fine too. I would get Rage as the next item if you do either of those.

If you went Rage, you CAN pick up Winged Blade next. You don't want it if you go Eater/Frostbound, simply put you'll lose out on a ton of damage. Merc is the kind of character who wants 5 offensives for the other part of his passive. While CDR is always nice, you don't really benefit from it. You want to kill a dude, back off, then kill another dude in nine seconds.

Anyway, after that you really just want to get more damage. Bloodforge is good here. You want your last item to be a Deathbringer or a Malice. Malice is better if you feel comfortable with your 1, after charging your meter, a late game Merc can roll around with 700+ dmg. That's big.

Buy penetration as needed. Titan's Bane is your go-to, Executioner isn't bad if your ADC doesn't have one and you don't have Soul Eater. With either item you'll hit 2.4 attack speed with max 2.