What are you encoding the TV Shows from? If you're ripping them from DVD, you should be able to extract the individual episodes as separate files... They're normally stored on different tracks on the DVD.
That having been said, MPEG Streamclip is a free application that should do what you want.
As for encoding the TV Shows, what aspect ratio are they originally in? A 4:3 TV Show (standard TV content) is going to basically be 640x480 off the source (DVD or broadcast), while a 16:9 TV Show (ie, HDTV/widescreen content) will likely be anamorphically 854x480. From a DVD, the original resolution is 720x480 regardless, and anamorphic encoding is used to stretch or reduce as necessary.
The problem is that the iPhone screen has a 1.5:1 aspect ratio. This is right in between the 1.33:1 (4:3) of standard TV content, and the 1.78:1 (16:9) of widescreen TV content, so you're not going to be able to encode anything to natively take up the entire screen without distortion. The iPhone does have a "zoom" feature (just double-tap on the screen when watching a video), so you have the choice of letterboxing or pillarboxing (depending on the original aspect ratio) or cropping off the edges in order to make the video fill the screen.
The 1.5:1 aspect ratio was likely chosen as a compromise between the two common aspect ratios, so that you could watch full-screen video with minimal cropping in either case. To be fair, it's not nearly as bad as trying to watch 4:3 content on a 16:9 screen, or vice-versa, so it's a very good compromise, in fact.
As for the preferred resolution, if you are only going to watch your content on the iPhone screen, I would recommend going with 576x320 (or thereabouts) for 16:9 content, and 480x360 (or thereabouts) for 4:3 content. This will provide maximum possible resolution on the iPhone's 480x320 screen for both types of content, particularly when watching it "zoomed" (ie, with edges cropped off).
That having been said, you may want to encode in 640x480 or 854x480 (anamorphic) regardless, as this will give you much more output capabilities if you do eventually decide to connect your iPhone to a TV or watch your content on your computer.