A record player cabinet, especially a vintage console, is delicate electronics wrapped in delicate furniture. Immobilize the turntable's moving parts first, then treat the cabinet like the fine furniture it is.
Pro tip: Back off or remove the counterweight and note the tracking-force setting so you can re-balance the arm correctly later.
Watch out: Never move a turntable with the tonearm unsecured; it will swing and destroy the fragile stylus and cartridge.