What solutions are available for generating video signal?
HDMI is kind of inaccessible to hobbyists; the signal requirements are quite tough. If your driving chip has a USB interface you could try http://www.mouser.com/catalog/specsheets/UFX6000-VE.pdf . Given the high data rate of HDMI, I don't think you're going to find a cheap solution. Built-in HDMI support on SoC is probably cheapest in terms of parts count.