Default US copyright law surprises owners: the CREATOR owns work unless a contract says otherwise. Paying an invoice doesn't automatically buy the rights. Good agency agreements assign work product to you on payment; read for that clause before signing, and demand it if absent (logos and brand assets especially).
Practical ownership checklist: source files delivered (not just exports), accounts in your name, licenses (fonts, stock) purchased under your business, and raw footage/photos included. 'We keep the working files' is a retention leash dressed as policy.
Agency non-competes on YOU (promising not to hire their staff or work with their other clients' competitors) deserve a hard look. Narrow non-solicitation of employees is common and fair; anything restricting who you can hire as an agency next, or what markets you serve, is not. That's a walk-away clause.