I bought my car with a bad tie rod end, and, let me tell you, it shook at all speeds, and wandered every which way it wanted to... or tried, at least. Occam's Razor suggests the tire, but the control arm bushing are very good at going bad (why do you think they sell the entire arm-with balljoints-for $62?).

Black/tan early '98 Contour SE Sport; V6, MTX, loaded
Kenwood KDC 316S CD deck; aux. dome light mod; trunk popper spring; resonator bypass; hood strut mod; SVT grille; Continental tires
Mom also has black/tan '98 Mystique LS; V6, ATX, Alpine CD deck