I haven't decided on the exact space I'm giving to Vista, but lets say 100GB. What partitions and what sizes (I'm very confused about sizes) for Ubuntu? I'm thinking as a minimum I should have /, /boot (for the dual boot), /home, and /swap. Given the number of non-distro apps I'll be using, should I include a /usr/local partition? If so, is a /usr partition suggested? Would a /tmp partition help with the computational jobs? File system types and sizes and partition types (primary, etc) would be great.
separate /tmp is rather useless in terms of performance if it is placed on the same drive as the OS and the same goes for /var and swap space. Also, they should be placed as nearly the start of the drive because that is the faster part.
/boot has nothing to do with dual booting so there is not reason to give it a partition of its own unless you will be using a filesystem that does not play well with GRUB (XFS, JFS and - for some distros - ext4).
What are non-distribution apps? If you use any of the more complete distributions, there won't be all that many applications that are not in the software repositories. And non-distro applications belong under /opt rather than /usr/local. Mine has stuff like netbeans, tomcat, eclipse and vmware server (FWIW, only the last one is not available from the repositories). I use separate partitions for swap, / and /home only because I find it a lot more convenient to manage.
Yes, filesystems make a difference. ext3/4: good allround and can be tweaked for specific purposes and has more features than the other ones; JFS great on older computers but not one that is receiving much maintenance; ReiserFS: fast for (very) small files but its future is uncertain; XFS: fast for large files, downside slowe file deletion but this can be tuned by increasing log buffers and tuning fs creation parameters (at the cost of higher RAM consumption).
Someone suggested I look into setting up the drives as a Raid 1. Is this doable with a dual boot? If so, would that make a copy of drive 1 on drive 2 whether I'm in Vista or Ubuntu? If not, is there a way to do that? Do I need to make any special partitions for Raid to work? Is there a good step-by-step setup guide for Raid (or whatever backup system people suggest)?
Yes, it's doable but if you are going to use windows RAID, you are making things more complicated. Linux is most reliable when use with true hardware or software RAID. Obviously, Vista is not going to make copies of Ubuntu or the other way round.
Special partitions? Of course. RAID1 requires that you have the same size partition on both drives so they can "mirror" each other. To increase performance, consider RAID0 instead - not much of a difference on small files but on larger files and applications, quite noticeable (for example, my copy of netbeans launches over 50% faster from RAID0); the downside is that RAID0 involves a higher risk of data loss and that RAID5 will combine the best of both worlds (speed and reliability).