Tilbury's biggest advantage over the south-coast cruise ports is simply distance — sitting on the Thames in Essex, it is one of the closer cruise terminals to central London, usually reached via the A13, which makes for a shorter and generally more predictable transfer than a run to Southampton or Dover. Weekday mornings still bring the usual commuter traffic, so an embarkation day that falls then benefits from a little extra time, but the overall journey tends to be more manageable than for the bigger south-coast ports.
Luggage is still worth planning for properly: cruise trips typically mean a full case per passenger rather than the single bag of a short trip, so telling us your group size and luggage at booking means an estate, MPV or 8-seater is booked from the start rather than assumed to be unnecessary.
As with any cruise departure, aim your pickup time at the check-in window your cruise line gives you rather than the sailing time itself, since check-in and baggage drop at the terminal take longer than boarding does.