There are many rolling shopping carts available that are designed with thick, robust rubber wheels ready for the cracks, cobblestones, roots, and ruts that are so common in many cities. Many of these carts have a larger weight carrying capacity than their slimmed down counterparts, but remember too that many rugged carts weigh more, so know your own strength and endurance limits.
Many rolling shopping carts can be sealed using either a zippered cover or even a solid plastic lid. These are great options for dealing with inclement weather, but keep in mind that such carts can usually tote less volume of goods. There is often some small sacrifice to be made when choosing a shopping cart, but if you opt for smaller storage capacity and don't end up with soggy, potentially ruined goods, then you made the right choice.
Also consider any special uses for which you might employ your shopping cart, such as carrying documents or sensitive gear like a camera or lenses. Carts with wire frames aren't ideal for carrying papers or for anything that could be damaged by even a small splash of water or dust.