Trademe is awash with used Freeview receiver boxes. Newer boxes may give you online features. UHF Freeview is better quality than satellite. Plug in via HDMI and disable overscan. Outputting 1080i to the TV would probably work best as it's unlikely to accept 1080p.
A 15 year old 768p LCD won't have great picture quality but it's an interesting relic.