I'm planning to buy a new LCD tv with Full HD and with HDMI inputs. My laptop (acer 5740) has HDMI output, but will Ubuntu support it?
The HDMI factor is not Ubuntu relevant, what you need to check is if your video card works with Ubuntu since the HDMI output will be configured using the drivers for your card.
Has a short answer: Ubuntu will support anything that your drivers will.
Your laptop has a Intel GMA HD integrated card that is supported out of the box by Ubuntu. I am assuming all the work it will be is to plugin your screen and configure the drivers so its recognized as a 2nd screen. It wont be very hard to do, maybe not as easy as in Windows ofc but, still doable and simple.