Best backup strategy for production systems

Hi,
I'm a newbie in postgresql. I've mounted my first postgresql instance, it
is empty now, only with default postgres DB.
It is under Linux, with 2 filesystems, one for data and another for
archiving (I've enabled archiving as it will be for production).
Could someone recommend me a strategy for backups, scripts and so on?
Can base backup be done with the system up (postgres up), isn't it?
Would it be ok if I do a base backup each week and archiving backup each
day?
As I've not configured backups (and archiving deletion), I've had my first
problem and it is that my archiving filesystem (FS) is full and archiver
process is showing "failed" with the last wal file copy (normal as
archiving FS is full).
Please, recommend me what I should make now .. I should create another
network FS for base backups and archiving backups? When I have my first
base backup, could I then delete archiving files, isn't it?
My archiving FS has 20GB, I don't understand as with a system without load
(it will be for production, but it hasn't databases now .. only postgres),
how it full the FS in a few days ... Is it normal?
Thanks beforehand.

Cheers...