The site gives very limited specs about your TV, aside from HDMI compatible there's no mention about other connection.
DVDs and Player is limited to 480p. However some new movies like Cars or Iron Man can be upscaled to 720p and produce better quality.
When you say RCA jack did you mean composite signal ( YELLOW wire ) or Component old name is Bitstream ( RED, GREEN and BLUE wire) which hold higher than 480 lines of resolution.
If your DVD have Component terminal at the back; use it instead of the composite signal. You can use regular RCA cords as long a you match the color of the terminal you are using at the other end. But your TV should support this connection.
Most DVD player now a days have Component signal Conectors but make sure your TV and DVD will match the frequency otherwise you are going to have a virtical lines or horizontal lines like on an old TV. However your new TV is LCD so hope you'll not have that problems just make sure you'll be able to return the player or at least exchange it when such issue occurs. Check if you can find a DVD player that can do up-convert.
Otherwise get your self a Play Station 3 or an Bluray Player that does upscale.