Receiver features
High end Yamaha Denon and Pioneer receivers have the "video format conversion" feature to take a composite video input and output over HDMI. Some, including the Yamaha RX-V2700 also over upscaling to 720p or 1080i. Most of these receivers are in the $1k+ price range.
It this is out of your budget, you should be able to get comparable video performance with non-HDMI receiver by connecting HDMI sources directly to the TV and purchasing an inexpensive switch box from monoprice for multiple HDMI sources. Get a quality upscaling DVD player like the Oppo DV-970HD ($150) to improve the PQ of your DVDs.