The Big Daddy type enemy first appears in Chapter 1, Level 2. This is the big, reddish meat crumbs type that shoots projectiles at you.
You'll encounter more than enough of them to accumulate 200 kills. Remember:
As you progress, you'll unlock better guns and perks. I'd personally recommend the Akimbo (dual-wield guns), energy shield (gives you one additional life when hit, regenerates every 20 seconds) and bullet time (slows time) for the majority of this game.