I think you can just unplug the old HDD, install the SATA HDD, load an OS onto it, and move files (not programs) from the old to the new. Not that it's as easy as it sounds!
WHATEVER YOU DO, spend the necessary HOURS reading all the instructions for each and every necessary step in this whole process!!! DO NOT start to work until you understand EVERYTHING that needs to happen and in what exact order. Otherwise this could become a weeklong project!
First, download Everest Home Edition(http://www.majorgeeks.com/download4181.html)and save it to the Desktop, then run it. It will tell you everything that's on the computer, like the motherboard, busses, all the geeky stuff. Save the report. Print out the whole thing for easy reference while you're checking into how you should proceed.
Also produce a list of all the software/programs, with their versions (find in Add/Remove Programs), that you want to use on the new Windows 7 HDD.
Next, go to the Windows 7 Compatibility Guide (http://www.microsoft.com/windows/compatibility/windows-7/en-us/default.aspx). I think there's a way on that site for Microsoft to probe the computer and tell you whether it will do OK with W7. You can then check the Everest report info and the software/programs list against their recommendations and decide whether to install W7 on this old computer, or to stick with XP.
Check out this tutorial in case you decide to keep the XP OS and want a clean install onto the new HDD: http://www.howtohaven.com/system/createwindowssetupdisk.shtml
I know nothing about the ramifications of using the SATA host PCI card, but I would read everything you can find about it before installing it. There are usually some unintended consequences to things that seem straightforward to start with.
As an intermediate computer tinkerer, I've successfully used xxclone (http://www.xxclone.com), a freeware program, to make an exact copy of one ATA/IDE HDD to another, including my XP Home SP3 OS. Make sure you fully understand how to use xxclone - their instructions are very good, but hard for newbies like I was.
This site's a great resource, too: http://www.rickmaybury.com/
Best of luck!