The things you generally don't want to trust a delivery service with until you get to know them are the types of products that require a subjective judge of quality before they go into your cart. Most delivery services keep their own stock separate from the grocery stores they partner with, and they only keep as much stock as they need for their deliveries. Even though their products are turned over and rotated more often than your supermarket shelves probably are, there are a few things you may want more personal control over.
Meat, deli meats, fish, seafood.
Unpackaged produce.
Some dairy products (eggs, gourmet cheese).
Perishable products and goods where you're not quite comfortable letting a stranger choose for you should stay off of your online shopping list until you're ready to test those waters. After all, there's no faster way to make sure you never order from a grocery delivery service than to order apples only to receive bruised, spotty fruit that you wouldn't have chosen had you actually gone to the store. The same applies for meat and seafood: if you're picky about the size and weight of the meat you buy, or how thickly your deli meats are sliced, you may have trouble giving up that control to an order picker who's responsible for filling a box with your order and putting it on the truck for delivery.
We're not saying you should never order these products from grocery delivery services. What we are saying is that you should probably hold off on them until you grow to know your delivery person, trust your delivery service, and fully understand your options to return products you're not happy with. In some cases, you may have to head into a grocery store to process an exchange. In other cases, you can just decline to accept that part of your order, and your delivery person will handle the exchange for you.
Still, if you know you'll never be happy unless you're the one squeezing the tomatoes in the produce section or you're a big fan of your local farmer's market or health food store, save the produce for a quick, personal trip, or beg a friend, neighbor, or family member to visit the store and choose wisely on your behalf. If the reason you're shopping for groceries online is because you'd rather put your time to better use, consider hiring a runner using a service like previously mentioned Fiverr to do the job for you.