Not going to bother with multiple Quotes, so just bear with me on this Post, I'll try to answer them all in the order they were posted and clear up any holes
You are correct with the term 'Dual Booting'. Others may comment otherwise, but since this is your first experience with Linux, trust GRUB (it's bootloader that searches for other installed OS's) with sorting everything out; in this case, it will know what's best. More on GRUB below.
Tremmor hit it with the partition types. There are three you need to know about: Primary, Extended, and Logical. One single HDD can have no more than 3 (4?) Primary or Extended Partitions. Logical Partitions are those created under Extended types. On the HDD1 I mentioned in the previous Post, Swap is the Primary. There are three Extended Partitions, and one Logical after that. Since you're running a single Drive, I would set it up like this:
Partition 1 (Primary): Windows (NTFS)
Partition 2 (Extended): Swap (Swap)
Partition 3 (Extended): /Root (ext3)
Partition 4 (Extended): /Home (etx3)
(Where NTFS, Swap, and ext3 are the types of file systems to be used.)
I would also suggest running Gparted from the Live CD rather than using Fdisk, as it offers a GUI as opposed to text-based Partition screen. Since you'd be running the Live CD and RAM, you can do pretty much anything you want to the HDD with it, as well as see a visual representation of the new partitions. Gparted will also be MUCH faster than Fdisk. Though, Fdisk is an awesome tool, so if you feel comfortable, go for it; just be careful.
The reason you are seeing the Windows partition on the Ubuntu desktop is because during Ubuntu setup, it will automatically mount all recognized (formatted) partitions regardless of whether or not they contain data. This can be tweaked during the Partitioning phase of Gparted, and it's called a 'Mount Point'. A Mount Point tells the software where a particular partition is located and what it's called. Anything with a '/media' in the mount point will show up on your Ubuntu desktop. On my Linux desktop, I have a direct link to both my personal XP drive (designated as Mount Point '/dev/sda/media/JasonXP'), as well as my personal Linux drive (designated as '/dev/sdb/media/JasonLinux). The reason you see the Windows drive on your desktop is because it's designated something like '<drive>/media/WindowsXP' (not exact, but general). If you don't want it to appear on the desktop, you can simply EDIT the partition during the install and delete the mount point. You are NOT deleting the partition, just the information that allows the Mount Point to be shown on your Desktop. Otherwise, it looks fine to me

I'd be wary of having a direct link to your entire Windows drive via the desktop, as it's easy to potentially erase key files, but so long as you're careful and don't access the 'Windows' or 'Program Files' folders, you should be fine.
A word of advice, it is
HIGHLY RECOMMEDED that you backup and personal files, pictures, documents, etc. to CD before playing with partitions, as it's very easy to mis-click something if you're uncertain and wipe one clean.
A quick word on GRUB... Assuming you have XP installed already and then install Ubuntu, the very last part of the install will look for other OS's. If found, it will install GRUB. GRUB acts in the same manner as Window's MBR, only does a much better job, in my opinion. After GRUB is installed and the Ubuntu install finishes, you'll need to reboot. Upon doing so, after your system POST's, you'll see the GRUB screen. From there, you can select what OS you wish to run. There's a default setup in the order it lists the options, but that can easily be changed by editing the file under Ubuntu.