Do I need a USPS business account to connect USPS?

Not necessarily. USPS has a Price Type setting:

• Retail (no USPS account needed): works with just the API keys.
• Commercial (requires a USPS payment account): also needs your USPS Account Type and USPS Account Number.

Required in both cases: Consumer Key, Consumer Secret and Ship-From ZIP Code.

Go to Settings → Store Settings → Shipping Setup, scroll to Shipping Carriers, tick USPS and click Save carriers. Then click Configure, fill in the fields, tick Enable for this store and click Save USPS.

USPS in Wcart gives rates and tracking but doesn't print labels.