The Toy Barrel is probably a franchise rather than a family business because of the huge advertisting campaign shown before the opening of the store in the beginning of the episode, and it is well known that the opening of a huge toy store or semi-toy store franchise location never go unnoticed.
In "Toy Store of Doom" SpongeBob, Patrick, and other fish go here to buy toys. When SpongeBob and Patrick find out about the toy store not being open yet, Patrick cries, until a construction crew finishes it.
The inside looks like a regular toy store. It has rows of shelves with toys in them. SpongeBob and Patrick got locked in the Toy Barrel in Toy Store of Doom. The counter with the cash register is located near the entrance. From this we can assume that there is only one register. Restrooms are located at the back of the building. It has many robotic toys and puppet toys.
The Toy Barrel is a huge barrel with a plaque on it that says "Toy Barrel" in yellow letters. At the beginning of the episode, nearly twenty children are at the front door waiting for it to open. It's entrance was designed to not let anything in, or, in this case, anyone out without unlocking it first.
The only known employees are Steve (cashier) and a security guard. The Toy Barrel could be a family owned business or owned by a franchising company.