Trying a live CD is the best way to start. Firstly, not every machine will run Linux, especially older ones as the hardware drivers have mostly been "reverse engineered" by some person dedicated to Linux. Hardware compatibility is getting better, but we try to avoid "bleeding edge" new stuff, as it takes a while before the manufacturer releases Linux drivers, or someone gets around to writing drivers.
But most machines have no trouble at all, so don't be afraid to try.
A Live CD is a Linux that runs from the CD. There is no install unless you decide you want to, using the OS from a Live CD won't cause anything to be written to your hard drive, unless you purposely do so. So you can't hurt your machine or it's previously installed OS by trying it.
(All these Linux CD's that you download come as ".ISO images" They can't just be copied to a CD, you need to tell your burning software that you want to "Burn an Image." The ISO image is like a Zip file. Or an "archive." Burning the "image" involves the software (say Nero?) "opening the archive and placing it properly on the CD so it boots properly. Simple step, but very frequently overlooked)
One thing to remember while using a Live CD is that it will run much slower than if it were installed to your hard drive, as any programs you "run" are decompressed and "run" from the CD and you are limited to the read speed of your CD, which is much slower than your hard drive.
But at least you can take a look safely, with no permanent changes to your machine.
Here's a link that shows you tons of Live CD distributions of various flavors of Linux: Live CD's
Can't go wrong with Ubuntu, it is taking the world by storm these days, and if you choose Ubuntu, the support forums are abundant.
I personally like PCLos, which is derived from Mandriva, which I also recommend. If you look at the list, SLAX seems to be the favorite, but I've not tried it and have no opinion.
Linux will run faster on your machine than XP, just because its designed to better use what hardware is available on your machine. But your XP running slow sounds like it might just be bogged down with adware, spyware, maybe malware and other nasties that steal your CPU cycles and hard drive use for their own purposes. Various free programs can clean it up, but nothing beats a clean install of XP to fix all those problems, then use the right free programs to prevent reoccurrence.
For the most part, the programs that you now use with WinXP won't run on Linux, but you'll find that there are usually at least two or more free Linux programs written to do the same thing, often doing it better. You find these programs by asking in Linux forums or googling "Linux equivalent programs" and the like.
You won't be able to download things faster, that is dependent on your ISP's package you are buying, not the operating system you are using.
Videos, DVD's and youtube things will work on Linux, although some distros get snotty about letting you play DVD's because of copyright stuff. but work arounds are easy to come by. Ubuntu I think is easier than some in this regard.
After you install Linux and are comfortable you "could" delete windows, but likely there will be an application or two that make keeping XP around worth the space on the hard drive. Especially if you are into gaming, as this is still Linux's weak spot. But if you clean up or reinstall XP, keep it. You (most likely) paid for it.
As far as space for Linux, when you install Linux you have to create a couple new partitions, (use the "custom partitioning" option when doing your install. You'll see your windows partitions there, and you can avoid overwriting them. If you just let the installer run, often it assumes you mean to use the entire hard drive, and it will overwrite your windows. Custom partitioning tools in Linux are robust, don't be afraid to use them, you'll find it not difficult to understand or accomplish.
When you are doing the custom partitioning, if will ask you want you want to do.
You need three partitions: the system files get put in what is the Linux equivalent of the "C:\" drive, called "root" and is represented by the slash: "/" You need a "swap" partition that is twice the size of your system's RAM. For you, one gig. Swap just needs created, you don't "format" it.
Then you need a place for "your" stuff. User files and downloads and things. This is called the "home" partition and looks like "/home"
Usually 4-5 gigs is enough for root, but can be 10 or so if you have lots of space. Same for the /home partition 4-5 gigs is enough, but if you have it, 30 is OK too. Once nice thing about modern Linux OS's is that they can now read and write to Window's NTFS files systems. They've been able to do that with FAT32 for a while. But today, with a Linux install, you can see and use your entire hard drive. So use some space for root, but what you do for /home can be pretty flexible.
Oh, another advantage to doing "custom partitioning" is if your Windows machine just has one big "C" drive, the partitioning tool can shrink your Windows partition to make room for Linux. Would be a good idea to defrag that windows partition before shrinking it.
One nice feature that every flavor of Linux has, is that by default, without you having to do anything, it will set up a "Boot Window" in your master boot record that will give you the choice of booting either operating system at start. It won't take much Linux experience before you learn how easy it is to manipulate the start up window and you can change the default settings if you want, so Linux starts without your intervention.
This might all sound complicated, but it's not. It's just different. After you go through this, you'll wonder what all the fuss was about. And you will really like what Linux lets you do with your computer. Looks nice too, even on older hardware.