Hey there, welcome. Looks like it will work. The card is low-profile ready, and you'll have to be sure you get the low-profile bracket along with it (edit: one of the product pictures
shows the bracket, so you should be fine there).
The PC has a single PCI-express x16 slot which the card will work in no sweat. It doesn't require external power, so you should be able to just pop it in, plug your monitor into it, and start up. You'll need drivers, but since you're not gaming you can just use the drivers that come on the CD with the card.
I do not understand what I do. For what I want to do I do not do, but what I hate I do.