Im a bit puzzled as to how you got to mpeg from AVI without knowing how.
That process is usually not automatic! (it takes
time and ties down the PC for a bit

).
Perhaps you "captured" from DV tape specifying mpeg capture "on the fly"
Its Ok if thats what you wanted , If not check the capture settings in the software.
Not knowing in which format you wish your video to end up the following are just general tips ( some of which have been hinted above ) I hope it doesnt seem repetitive ,If anything Im just reinforcing the advice
Ulead Moviefactory4 ( as mentioned above) will allow you import either mpeg or AVi and with it you can easily trim off bits before turning it to DVD (if that what you wish)
If you want to recapture as avi from tape, any video editing software can do the trim ( including WMM or nero vision) : you can output it however you wish or simply play it on the PC. WMM will not do DVDs .For that youll need Nero vision or a DVD authoring software.
If you get the bug to do a proper edit ( not just trimming a few "private " seconds

off) , for mpeg, there are mpeg editors ( Womble ( im a recent convert) and for everything else (AVI ) there is ample choice of software editors beyond WMM.
Most of these will edit mpeg as well but theyll probably reencode.
The reencoding will mean you dont save time ( by starting as mpeg) and your video PQ may drop.