I'm no pest control expert, but I've lived many years in homes with below grade basements, and bugs happen. They look like ordinary black beetles to me. The little black things might be their feces. Do you see legs on them? Get rid of the cardboard boxes for storage and get some plastic tubs instead. Or at least get the boxes up off of the floor. Some bugs are attracted to cardboard and like to eat it. I don't think you need an exterminator unless you're finding hundreds running around.

I think the big one is photo 2 is a pillbug/rollypoly/isopod. (Nothing to worry about. Sometimes they get inside and don't do well.)

The big one in the last photo is a beetle of some sort, but not something famously bad. Probably another case of being in the wrong place at the wrong time.

The little guys? They all look the same. It's possible that they were in the box you used, possibly as eggs. They hatched, and kicked the bucket. (Can you see any wings? Wings would indicate adults and wouldn't work with the Eggs In The Box Theory.)

I wouldn't worry about it. None of them set off flags for me as being bad house critters. They totally look like things that got stuck in a box.

Of course there are basements and then there are basements. Some are closer to nature than others. :)

(If you can zoom in on the little ones, someone might be able to ID them for you so that you can really relax about them.)

Thank you so much for the help! We are currently in the process of moving all of our things into plastic bins on shelves and getting rid of the cardboard, so hopefully that will make a big difference!

It will help! Cardboard boxes get gross no matter how good they start off!