Obviously, it all depends on you and the place you live.
That said:
Wald folding baskets are pretty indispensable. They're made to fit U.S. grocery bags and they can carry
lots of weight. Get the silver galvanized, not the black or white painted -- the painted ones rust. You definitely don't want the weight on the handlebars. Put it on the rear rack.
As for the bike: My pick for a grocery-getter would be an '80s Japanese or French sport-touring bike, with the drop handlebars swapped for upright bars (North Road, moustache, or albatross are good choices). Get something like this (in your size, though) and swap the bars:
https://southjersey.craigslist.org/b...505083409.html
They often have stem shifters, which makes the handlebar swap easy (if not, you can easily switch to friction thumbies or bar-ends).