Case insensitive searches can be achieved by using the -iname switch
find /home -iname '*.mpg' -o -iname '*.avi'
Let'search for .avi files bigger than 700M. This can be done with.
find /home/ -name '*.avi' -a -size +700M
Now, let's find the same subset of files that were modified less than 15 days ago
find /home/ -name '*.avi' -a -size +700M -mtime -15