What suit style(s) should every man own?

For an initial suit, a navy 2-button or 3-button suit (depending on your build) with notched lapels works for every occasion (at the office, a party, a funeral, a wedding, etc.).

From there, it's all about your tastes. Branch out to different colors (medium/light blues, dark/medium/light grays, brown/taupe/tan, etc.), different patterns (pinstripes, plaid, windowpane, check, birdseye, etc.), different cuts (slim, athletic, classic), different vents (center, side, unvented), different lapels (peak, narrow, wide, etc.), etc.

I do like my Sears Pinstripe Suit.

If you can only own one, a navy blue classic cut business suit (can also use the jacket separately with khakis or other pants). If you can afford a few more, a black or charcoal one and a summer suit (linen).