Brompton will be best for holding your shopping since the luggage goes on top and the folded bike is bottom heavy.

Carry-me is good too, but you can't use the large luggage capacity of the rear rack in the folded position and instead have to use the front luggage rack or hang bags off the seat or handlebars. Plus it's a little top heavy while folded.

Strida and Tikit both roll along nicely without their luggage capacities being compromised by folding, but they both have to be balanced because they roll on only one or two wheels instead of three or four like the Brompton or Carry-me.

Dahons and such can also be rolled with some effort, but the balancing act is even more difficult and a real hassle with luggage IMO.