Probably make the swap a gig or two (you have plenty of ram, but disk space is cheap and it's cheap insurance). There is no '/swap' though. It doesn't mount anywere the OS kernel uses it directly. It's not like the swap file in Windows,
it'll use the partition raw as it has it's own format.
So Linux needs a minimal 2 partitions to be installed generally. A / (root) partition and a swap partition. Those both would be on your 18 gig disk.
I am assuming that your using software raid for everything... (so that makes a difference if you throw some hardware stuff in there)
For each drive you want to use in the raid arrays you will partition them into one big partition. Then you use those partitions as devices to build the raid arrays.
For the disks in their paticular RAID arrays they will end up as /dev/md0 and /dev/md1 and /dev/md2. I don't know which would be which, I think it matters only in the order you create them. So lets assume that the 2 120 gigs are /dev/md0, the 2 60 gigs are /dev/md1 and the 2 36 gig scsi drives are /dev/md1. You don't need to partition the raid devices.
So then you would use /dev/md0 and /dev/md1 as Physical Volumes (PV) you combine to make the Volume Group (VG) that will be divided up in Logical Volumes (LV) by the Logical Volume Management (LVM) stuff. You can make the entire thing into one big logical volume if you want, but you can also divide it up into various logical volumes depending on what you want. They are resizable and dynamic (weither or not the actual file systems on them are also is another matter).
So you can do things like leave a bunch of unused space if you feel like it that can be allocated later for different purposes, but it may just be a pain for you later if you want to use it all for storage.
Then you just format the /dev/md2 (the 2 striped scsi) and use that like that, like it was a regular partition or whatnot.
Now you can do something like mount the storage logical volume as /storage and mount the striped array as /data if you want and configure Mythtv to use them, or you can find out what Mythtv uses by default and then mount them on those directories. It depends on the default configuration of mythtv, but you can ultimately do whatever you want.
So the only question that is realy up to you is do you want /home to be a logical volume in your storage or do you want /home to be on the same disk as root?
It's nice to have a /home partition or volume as you can save setting and user files in between OS installations. It's not nessicary. Whatever you think would be best.