You'll need an HDMI cable. I know 4K blu-ray players need a 4K-rated HDMI cable (HDMI 2.0). The Ultra streams 4K, but don't know if HDMI needs to be 4K. Would think so. Prices on cables are low enough that you might as well get the 4K-rated one anyway. Most are probably already rated for it.

The Ultra supports WIreless 802.11ac while the Express only offers 802.11b/g/n - so theoretically, yes, the Ultra would offer better connection speeds. However, it also depends on the speed of your internet and whether your router supports Wireless AC. I've also heard of people having issues with any brand of streaming player (Fire, Apple, etc.) on older TVs in general - I think in these cases it might be an HDMI issue (perhaps faulty) - where the video is reaching the streaming player quickly without issue, but the TV is having an issue processing it at the HDMI port. All of my older 1080p TVs have had issues with HDMI ports over the years. Usually going out completely after power surges.