I would generally want all the files contained in the tarball to be in a directory, and for that reason would use tar from /home ...
% cd /home
% tar cjf /path/to/backup/archive-$(date +%F).tar.bz2 username
The point to keep in mind with tar is that it is an archive of the target path, so /home/username will contain a 'deeper' directory structure than "." .. this can have repercusions if/when you untar the archive.
There are many way to read the content of the archive, 'tar ztvf archive.tar.gz', or using less (with lesspipe.sh) but people often overwrite files and/or end up with files strewn in unwated places (hence the '-w' switch).
Also useful ... send the data directly to another machine (tar over ssh)
I find rsync much more flexable for this sort of thing and so rarely make backups of this sort.
tar cjf - username | ssh firstname.lastname@example.org "cat > /path/to/archive-$(date +%F).tar.bz2"
HTH ... khay