Basically NTFS is Microsoft's replacement for the FAT32 filing system, which offers several advancements including increased security, file encryption, and better compression. The only downside to NTFS is that it is not compatible with older operating systems. Thus, if you plan on having a multi-boot system, or want to network the computer in a mixed OS environment, FAT32 is your best bet. Since this is a standalone computer being setup for your aunt, it doesn't really matter, but I'd still suggest NTFS as it truly is the superior format.
But you don't have to take my word for it...check out this handy Microsoft guide which compares FAT, FAT32, and NTFS file systems to help decide which one is right for you. Then for a nice table comparing the "specs" of each file system, as well as their limitations, click here. Finally, to satisfy your inner geek (no need to hide it...you're among friends ;)), check out this research paper written by computer science student at the Milwaukee School of Engineering.
Hope this helps,
My aunts computer is a HP Pavilion 6645C with 564MHz Intel Celeron, 320MB of RAM and a 20GB Hard Drive. Now her computer came formatted FAT32. I will be reformatting it for her soon. Non of the HP "original" stuff will be placed back onto her computer. I know quite abit about computers but I do have my weak spots and this is one. Now my questions is this. Will her computer hold NTFS format and which is better to use NTFS or FAT32? Also if one is better than the other what's the reason's? Please only the people who know the answers to my questions for a FACT respond. Im not try'n to sound mean or anything but this needs to be done soon and I dont want to have sort threw a bunch of people bumping heads together over this all.