Find the dimensions online. Check the makers website, or wherever you bought it from. Newegg most of the time has those measurements. Since video cards recently have been getting longer, it's become standard to list how long a card a case will accept. Having said that, the card you linked is extremely short, I'm 99.99% sure it will fit. I have no idea what your case is like, but I'll bet the bank it fits.
If you were looking to upgrade your PSU, I would do it, personally. Rosewill is not known for quality items. Give us an idea of your budget.
Also, I absolutely love this website when it comes to video card reviews. It's based in UK, and they don't get everything there is, but they do some fantastic graphs and performance tests. Fan noise, which is a big deal with a HTPC, power use. All kinds of things. I haven't been in the market for a card for more than a year, but I was just checking it out after reading your post. They have a new thing where they rate the performance per wat, and per dollar. Which, when you compare whatever card you are aiming at, puts a good perspective on things. Maybe there are other sites that do this, I don't really look through reviews very much.http://www.techpowerup.com/reviews/HIS/HD_7750_IceQ_X/
I found a card they reviewed that uses the same chip, it's overclocked at 900mhz, where your link is 800mhz. Review card is also only sporting 1gig, where yours would be 2g. The difference won't be huge, you can get a general idea from the other cards on how it performs.