You'd have to have scopes and such, and even then, it would be a bit difficult to see the advantage of 1080p over 720p with a 20" or 25" display. However, you do need Blu-ray discs (and therefore a Blu-ray disc player) for true 720p resolution; DVD only stores 480i resolution.
It should be noted that there is as little difference between component video cables and HDMI cables, with regard to video quality, as there is between 1080p and 720p on a 25" display (i.e., insignificant or no difference). The difference between component cables and HDMI is really a matter of five wires instead of one wire, and with regard to advanced capabilities, such as HDCP and HDMI 3.
HDCP is required for pass-through of video. So, for example, if you're directing your video through a receiver (in hopes of having the sound go through your surround sound speakers), you typically need to connect the Blu-ray disc player to your receiver via HDMI, and connect the receiver to your display via HDMI. Otherwise, you'll get a copy protection error message. (HDCP may also someday soon become required for selective output controls technology, but that will only affect broadcast, not disc.)
One advantage of HDMI 3 is additional switching capability. I would benefit from HDMI 3 because it automatically switches my display between 2D and 3D. However, I can just as well do that switching myself, manually, using my television remote. Regardless, with the low-end television that the OP has, HDMI 3 is not a consideration.
To be clear: Component cables can transmit 1080p just fine. If there is any impediment in that scenario, it is imposed by the source or destination device - not the cabling.