Ethernet cables are shielded, and have no issues with range ... a Cat 6 cable should be sufficiently futureproof. Feel free to use Cat 5e, however, if you're trying to save money.
see HDMI cable types. Cat1 and Cat2 are unofficial voice grade standards, while the rest are based on the EIA/TIA-568-B standards. Ethernet wiring today starts at Cat5e. Cat8 is for short ...