I have a total of 5 users on my Linux machine. Right now user 1 is able to browse other users home directories. I want to change this permission for all users except root. I want users to only be able to read, write, execute to their own home directories.

Is this possible and will this cause problems with applications like Firefox and or anything else?

The only reason why is because this machine is a very large FTP box and I don't want users snooping in other directories if they upload personal files or photos to their home dir via FTP.

Can someone please explain to me the best possible solution in this case?

Thanks!

It is definitely possible, and is the default configuration on many systems. I don't forsee any problems with anything - users will simply not be able to the home directories of other users.

A simple "chmod go-rwx" on each directory will remove read, write, and execute permissions from the owning group and other users - only the owner of the directory and root will be able to use it.