How can I be sure I am getting the best picture possible?
First, start with your TV. If the TV's picture isn't very good, DVD software won't look very good either. There are a couple of instructional DVDs that show you how to properly calibrate your TV to look its best. Among other tips, these usually involve turning down the brightness and sharpness controls, as set manufacturers tend to increase both at the factory to maximize visual impact on the sales floor.
Now that your TV is good to go, you'll want to use the best output from the DVD player to your TV. Most DVD players offer HDMI, composite, S-Video, and component video outputs. If your TV has an HDMI or component input, use it. S-Video, which separates color from black and white signals, can provide up to a 60% sharper picture over composite. The film-like quality of both component video and HDMI is the best of all.
Most A/V receivers/processors allow you to route your video signal through the receiver to the TV. This provides the added convenience of on screen graphics and video switching, but at the risk of slightly reduced video quality. To obtain the purist picture, many videophiles connect their video sources directly to their TV after they've used the on screen graphics to do their initial set-up.