That was one of the best on today's market what I just showed.
Well, I have ATI Radeon HD 4870 X2 and it doesn't require Blu-Ray drive to work. (I have some old DVD drive, which I have had as long as I can remember...)
I think what they mean by that, is that if you want to get everything out from your card you'd need HD monitor and Blu-Ray drive (Blu-Ray movies = Full HD [1920x1080] resolution and HD monitor to see the HD quality), but it's not really needed to get the card to work (lower resolutions work as well
).
Just Google your monitor name and see if it supports HD resolutions (1280x720 / 1920x1080).
But if you don't have HD capable of graphics card, even if you're monitor is, you can't use these resolutions (I believe...).
And what comes to your CD/DVD-drive, just check the front panel to see if it says: CD, DVD or Blu-ray.
You gave link to HD 4770, I have just newer version of it with 2GB memory and it works fine for me, so I suggest you to get either that or put little bit more money into the card and buy a newer model with higher memory.
Here's one card with 1GB of memory. (Price: £118)
But remember, I'm not a pro, so you should give a try on some of the other forums as well and see what other people suggest.
Also, one thing you can do is go to YouTube and search for the graphics card you're interested and the game you want to see to be played on that card. Also, set the words "maxed out" or "maximum graphics" / "settings" to see how the game works with full graphics on the card you're looking for.