What I fine works best for me is using ME, using yellow tags for checked bags, letting Disney handle my luggage and ordering from Garden Grocer. I find this to be the most relaxing and less stress. (might not be everyone's choice).
I have done both ME & Car Service with and w/out grocery stops.
I do not find Car Service to be that much faster than ME. You greet your driver, go to the luggage carousel, wait for your luggage, pick up your luggage move it to the car and get in the car and drive to the resort.
With ME you go to the ME counter, check in, short wait for the bus, and your off. At times you will have to stop at one to two resorts before yours. But your not having the hassle of dealing with your luggage at the airport. So I find car service to be slightly faster, somewhat depends on how fast luggage comes off plane to carousal.
My yellow tagged checked bags have always been delivered in less than three hours after arriving and usually they are waiting on me in the room or at the resort before the room is ready for before I am ready to go to my room.
I have also done car service with grocery stop, which in my mind negates any time savings. I do prefer to use Garden Grocer. As your order is delivered right to your room. No hassle of stopping at a store, while family waits in car. You pay a delivery fee and prices are probably higher than Wal-Mart. I also dislike grocery shopping and to not see a Wal-Mart, Publix etc. on vacation is worth the $14 delivery fee.
I might be the odd ball, but I actually like seeing what other resorts look like when dropping off other ME guests. For example the only time I have seen the Pop Century was when it was a stop on the ME.
I also love the convenience of checking bags in lobby and checking in for your airline when departing right at the resort. Although I think you can do this even if you do not use ME.
There is something Magical about landing at MCO, knowing you are at your place of leaving the real world and starting your Disney Vacation by being greeted by ME staff, boarding the ME bus, watching the cartoons and park videos...etc.