It is an old joke but actually true - as I told my German housemate in 2019 when this started -
Buy Toliet Paper it always goes first because it does.
Cat Sand (litter in the USA) - if you have cats start getting lots (it tends to be one of the first things to run out) if you don't have cats buy one or two bags if you live near where things get icy as it works on sidewalks and porches to prevent falls.
Spices and flavorings - especially cinnamon, cloves, ginger, and nutmeg. Also, vanilla (real) pods or extract, and basic herbs if you don't have a big garden - especially Rosemary, Oregano, Sage, Cumin, Chili Powder and consider some powdered onion and garlic.
The above will go a long way towards making packages of dried beans, rice, and pasta less boring and you can cook with them.
Yeast, Baking Powder, and Baking Soda - and if you don't know how to use those yet (we all start somewhere) start doing some practice baking.
Good General Cookbook - my husband had to take over nearly all the cooking this past year for various reasons and while he knows how to cook a lot of fancy stuff, having a basic "how-to" for usual stuff was great. Since you never know when a family member who has never boiled water may need to cook in a pinch - or your partner previously mostly did fancy stuff - this is a wonderful thing to have.
Actually, there are so many good sites on the internet, you can also download a lot of stuff but be sure to print it out or hardcopy in a book (I've had my blue book since the 1970s).
Suggestions: The New Fanny Farmer Cookbook (early 1990s edition) The Joy of Cooking (1950s or more recent edition) on this side of the water any of the Mrs. Beaton's Cookbooks (updated ones) and a lot more (The Pioneer Women has a great website and cookbooks, as well as being on TV now).
Wheat Flour (or whichever flour you can eat) and/or wheat grain and a grinder. Organic unbleached flour will last up to 2 years in my experience, whole wheat flour about 6 months, regular white (bleached flour) five years or more (but is mostly just calories) and whole wheat grain can last a few thousand years (we just finished the y2K stuff last year).
(hint the wheat harvest mostly failed again in North America which is where most hard wheat comes from).
Bulk bags (or a lot of small bags of):
Rice (25-pound bags make about 3 or 4 average-sized plastic buckets or you can use totally dried plastic water jugs for storage).
Dried Pasta - get the real stuff from Italy if you can, it will probably last several years if stored properly.
Cornmeal - if your family can eat it
Legumes that need soaking - Pinto, Kidney, Black, garbanzo beans (aka chickpeas) other dried beans
Legumes that do not need pre (or much) pre-soaking - split peas (yellow or green) lentils (all colors)
Canned Tomatoes and Tomato Puree/paste - if your family can eat, buy as much as you can - the cans last about 4 years in a really wet climate like ours, cardboard containers about one year. These can be used for all sorts of things from pizza to soup and of course pasta.
Bleach - the backup plan to purify water and to sanitize surfaces
Oils - Olive oil (keeps several years), lard (in the freezer), coconut oil, vegetable oils (as backup), and Crisco for long-term storage/back up (not especially healthy but will do for cooking in a pinch, the same with the vegetable oils).
Oils, like the spices and flours, will go a long way towards keeping food "interesting" and tasting good, even if you use it sparingly.
Dry Pet food - most dried foods will keep at least a year (cat and dog) again not always the best option but will keep them fed.
Sewing and Crafting Supplies - these run out quickly as we discovered in Ireland and are not considered a priority by shops but you will want them for repairs and keeping sane.
Mentionables and Unmentionables. Underwear - socks - bras, shoes, hats (and some yarn/needles to make more), ours are finally running out and it has been very difficult to find new cotton anything at least here, even online. We managed but they do wear out and are difficult to repair (especially ladies' underwear).
Basic Home guides:
Basic Repairs, Sewing, Knitting, cooking, gardening, etc.
I could go on but I'll end this for now with a copy of any of the later editions of:
The Encylopedia of Country Living by Carla Emery
Knitting Without Tears by Elizabeth Zimmerman
The Hassle-Free Make Your Own Cloths HandbookThe (on Kindle - the original is from around 1970)
There's a lot more, but that's enough for one post and again we all start somewhere.
Don't be scared and also see what you buy every week, month, six months and start by buying 2 or 3 instead of just 1 item if you can. That's a great way to get a pantry going.
Edited to add: while this thread is mostly about the lockdown and a lot of these suggestions are basic prepping 101, some of these things we did run out of Ireland - including things like underwear, cotton PJ's, flip-flops (I can't find any), bread bakers, and for a time, freezers, fridges, stoves and a lot of smaller stuff like slow cookers because scarce or difficult to fine.