It *should* be as easy as

Create the partition(s) on the drive(s) and create the filesystem(s) you
want.
Create a mount point for the partition(s).
Do a chmod 777 to the mount point(s) to give everybody global permissions.
Mount the partition(s) to check that everything works OK.
Edit fstab with the details of the new partitions(s).

Alternatively, a chown to the mount point(s) *should* change the
ownership or a chgrp *should* change the group (remember to do all these
as sudo and to add yourself to the relevant group if you take the last
option).

Note, *should*... Most times I've done this (which, admittedly, isn't
that often) it's worked like a charm but, just ocasionally, the chmod
doesn't want to 'stick' when the drive is mounted.

I'm afraid I have no advice to give you as to how to get it to work if
the above procedure fails as I have yet to find a systematic way of
sorting it out - it seems to be more of a black art than a science, I'm
afraid.