MDF vs plywood vs solid wood: which sheet goods should I cut for which project?

MDF

• Machines beautifully: dead flat, no grain, no tearout, crisp v-carves.
• The catches: the fuzzy carved surface drinks paint (prime carved areas with a shellac-based primer or thinned glue, or they look forever fuzzy); zero water resistance (swells like a sponge, so indoor only unless fully sealed); the dust is the nastiest (respirator + collection, see the safety entry); heavy; screws hold poorly in edges.
• Best for: painted signs/decor, templates and jigs, spoilboards, prototypes.

Plywood

• Strong, dimensionally stable, real-wood faces. The go-to for structural parts, boxes, furniture.
• The catches: veneer chip-out (downcut/compression bits, see the fuzzy-edges entry); v-carving exposes the ply layers as stripes, so embrace it (Baltic birch edge aesthetic) or avoid v-carving plywood faces; internal voids in cheap sheets surprise you mid-cut; thickness is never nominal (measure! "3/4" is ~0.70 to 0.72").
• Grades matter: Baltic birch (many thin void-free plies) machines far better than big-box sheathing.
• Best for: cut-out parts, boxes/joinery, layered projects, painted decor with routed (not v-carved) detail.

Solid wood

• The only choice where the carve IS the show: stained v-carve signs, 3D reliefs, cutting boards, heirloom work.
• The catches: movement (acclimate; expect seasonal change), warp/cup (flattening pass), grain behavior (see the species entry), cost.

Quick decision

• Painted? → MDF (prime the carve)
• Structural/parts? → plywood (downcut bit)
• Stained/natural carving? → solid wood
• Outdoor? → solid cedar/white oak with an exterior finish, or HDU (see that entry); never MDF.