In the US and Canada, you would typically pay between US$12 to 25 for an initial order of 250 checks, in 5 books of 50 each. This includes the register and check book case. The checks have your name, your address, unique bank account number and bank routing number on each check. The bank will NOT refund your money for any unused checks.
In fact, you need to shred or otherwise destroy the old checks from Bank A as soon as you have closed out the account and confirmed that the transfer to Bank B is complete. The old checks are a potential risk, should anyone with fraudulent intent find or take them from you.
Some checkbook cases are worth keeping and re-using. You can do that with the new checks, as the sizes are standardized.