on TV, movies... basically, typically what professionals do. Hard cuts, fade-in/fade-out, dissolves.
In Music videos, a *long* clip is maybe 2-3 seconds.
Sorry - can't help you with Vegas on the audio portion... other than, if the coughing/talking is not during a key part of what might be important to your friend (or friend's daughter), have a music sound track - just kill the background noise. If there is dialog you want, fade the music out and bring the dialog in... and when done, fade the dialog and bring the music back.
If you want a long speech that has all the background noise, that *could* be a challenge. You will need to strip the audio out, bring it into an audio manipulation application (I have used [open source] Audacity and SoundTrack Pro [Mac only]). The crowd noise is not so tough, (take a sample and filter) but the coughs can get tedious because I have found you need to work them individually.
If you are concerned about music royalties/copyright violation issues, there are a couple of royalty free sites out there - I've used www.incompetch.com ...
Right now, I am putting together a video for my friend's daughter's graduation and am wondering what types of transitions or audio effects you like for this type of video? Do you use fancy flipping transitions or simple fading? Also, I am trying to find a way on Sony Vegas Studio how I can cut out background noise (i.e. people talking, coughing, etc.) so I can hear the subject clearly. (I know an external mic should have been used, but...) Thanks for your suggestions!