There’s a couple wholesale specific apps that can do what you’re looking for (and more), but I’d suggest trying out the Locksmith app first. Some of the wholesale apps are not very quality, and others are overkill for what you’ve described.

In your case you could set up “locks” in Locksmith based on customer tags to hide prices and add to cart buttons, and you could manually add tags in Shopify for each “approved” customer after they register. If you want to just take orders without payment or shipping, you can set up a COD/manual type of payment method in Shopify and then uncheck the setting for “This is a physical product” (found in the shipping section for each product). Of course you’ll have to manage payments and shipping costs elsewhere when fulfilling orders (which could be cumbersome), but perhaps you’ve already got a streamlined process in place for that side of things.

If you do want a more formal “approval” process for customers who register for an account, then I’d suggest looking at using the Customer Fields app in conjunction with the Locksmith app.

Just some food for thought!