Although models like the golf bag styled upright Hod trailer are attractive for their compactness, the high shopping load means they can overturn on cornering. They also have the disadvantage that vertically stacked shopping does nothing for soft or fragile items like eggs and bananas for example.
So the main things to look for are low load, quickly detachable, a detachable link that isn't very flexible, since that type causes disconcerting push-pulls on the rear of the bike while cycling, and light weight.
However, a golden rule first. Since trailer wheel rolling resistance adds substantially to the cycling effort needed, even on the flat, a trailer should never be used for a load that could conceivably be carried on the bike. The right large panniers can carry four to six supermarket plastic bags full, and any boxed items bought can be bungeed in a carrier bag onto the carrier top as well. You can even use front panniers as well.
I've only used a trailer on very rare occasions for food shopping, and most of those with a very small trailer for a Xmas shop or similar.
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