When you get to Demuxers expand the category (in the left hand pane) and you should find AVI in the drop-down list
Is there a way to compress it without doing harm or are AVI files always huge?
They are if you do not use the transcoding option.
You could try in VLC:
Media->Convert / Save->Capture Device:
Set it up as previously
Click Convert / Save
Add destination file
If required (or just select from pre-built):
->Create new profile (adjust to suit)
Name = Video - AVI
Encapsulation = AVI
Codec = MPEG-4
Bitrate = 8000 kb/s
-Keep original audio track (tick)
Select profile Video - AVI
Press Start button to begin.
I personally prefer to capture without transcoding (storage space permitting) as my machine is not quite up to transcoding on the fly.
I would then use another transcoding program to reduce the file size.