It is never a good idea to delete your original files - I wouldn't even risk opening or utilizing irreplaceable original files except for the purpose of backing them up by duplicating them or burning to CD/DVD. Unless you can very easily replace a file in the event of damage or a need to transcode to a different codec or with different settings, you should always keep your original files safe. With a copy or two of your original tucked safely away on a backup disc there's no reason you couldn't (or shouldn't) delete the source file after transcoding. Compressor doesn't have a built-in function to accomplish something like this, but any preset you create can include a post-processing Applescript. I haven't investigated this option in depth, but it might be possible to to attach a script that deletes the source AVI on completion of the batch. Saving your preset as a Droplet lets you transcode a batch of files with drag and drop ease without launching Compressor (there are some options in the Droplet configuration that enable a Droplet to do its thing without any further user action).
Whether you "should" convert your AVI clips to MPEG-4 for streaming is something only you can decide. Presets for MPEG-4 optimized for streaming at a variety of data rates are provided by Apple in the "QuickTime 6 Compatible" Streaming group. You can try the entire group on one of your AVI files - drag the source AVI into the batch window (name the batch in the field at the top if a name isn't automatically filled in) then drag the entire Quicktime 6 Compatible group onto the AVI file entry. Submit the batch and Compressor will go to work producing a new video file for each of the presets in the group. When it's done, open the finished MP4s in Quicktime Player and check them. Any that are not up to your quality standards can either be eliminated or settings adjusted (don't change Apple's original presets - duplicate the one you want to adjust, rename it in some way, make the desired changes and save).
After some testing you may decide that MPEG-4 isn't the best for transcoding your files. MPEG-4 is terrific for DV video from the typical miniDVcam edited with and exported from iMovie/FCE/FCP. But since MPEG-4 is a lossy compression scheme, you may not get the very best result when your source is an already highly compressed MPEG-4 format. You'll have to test and see what works. MPEG-4 is widely accepted though and there aren't many PCs or Macs that wouldn't be able to play the files. If you want to use Compressor to batch your transcodes, MPEG-4 is probably your best bet. You're bound to get flak from someone (who can't play the files) about your choice of format, but at least if you check with a modest sample of your target audience (friends? family?) you'll have an idea of what to expect.
The Apple provided presets for H264 transcoding are in the Web Streaming Quicktime 7 Compatible or Web Download Quicktime 7 Compatible groupings. H264 produces amazing quality at large frame sizes, modest data rates and quicktime movies that are of manageable size. But even on a very fast Mac, H264 is very slow to encode. You'll have to make some tests and decide if the time to encode is really worth it. In any event, H264 is still so new you may be shutting out the vast majority of potential viewers of your videos if you provide only H264 encoded versions.