Most people probably take S and A/C/E train from Grand Central to Penn Station. However during Peak hour or packed cars it is challenging to fit in. Even during Off-Peak hour the subway cars are never designed to accommodate luggage storage. You could take taxi, Uber, Lyft, or any private transportation service though it may be expensive way. One possible solution is to take LIRR (Long Island Rail Road) that is equipped with overhead racks, transfer at Woodside station.
This video shows wheelchair-friendly path to also include elderly, disabled, and people with luggage, starts from 47th Street and Madison Avenue, Northwest side of Grand Central Terminal (Grand Central Madison - LIRR Concourse). From Main Concourse (that is closer to S subway station) simply go north through underground tunnel. Check out the followings for details.
• NYC Grand Central Term...
• NYC Grand Central Term...
• NYC Grand Central Term...
Grand Central Terminal and NY Penn Station are two train hubs not yet integrated. There is a plan to extend Metro North train to reach Moynihan in reducing people's volumes in subways, and to interconnect the two busiest stations in NYC as Midtown Manhattan evolves.