If this is a production server I wouldn't use ext2. In the case of a
crash or reboot, you don't want to loose precious uptime just because of
fsck or corrupted file systems.
Doesn't need to be separate but could prevent a runaway process from
filling /var just because it is spamming log entries. Could also be
achieved with quotas.
If you worry about waste consider bind-mounting both from the same
partition and install quotas to avoid one filling up the other. A bit
like poor-man's btrfs sub volumes.
Since you are using LVM you should also keep some unallocated memory,
start with smaller partitions and monitor usage. A cron job that looks
at `df` and sends a mail when a partition is more than x% full helps a lot.
Restoring from lvm snapshot is like restoring after a black out or
similar crash. Having proper dumps is always a good idea.