Ok Jim. Like you I wanted to go to a 3 screen setup and, already having a 27" monitor running at 60hz, i got myself 2 more of them and made sure that, even though they weren't exactly the same model, they ran the same resolution and refresh rate.
From what I have read about what monitors you have (or are getting) they seem to be fine. I also had an HDMI cable for my first monitor and, again like you, thought that I could use this as one of the connectors. Unfortunately it wasn't so straight forward and after many hours of research, asking around and tearing my hair out, I finally figured out how to get it all connected correctly. You need to connect 2 of your monitors (left and right monitors in my case) using DVI cables. Be careful when buying these as the ports on the back of the card require two different types. One of them is DVI-I and the other is DVI-D.
My cables are Single Link only because I didn't know there was this kind of difference until researching for this post.
but I can't see it being a problem if you used Dual Link cables instead. The choice is yours.
The way I connected my centre monitor was decided as I already had the HDMI cable I mentioned earlier and after finding out that using it direct to the HDMI port on the card wasn't working I found out that I could get it to work correctly by getting an adaptor to convert it to Display port.
If you don't already have an HDMI cable then you can get a DVI to Display Port cable to connect the 3rd monitor to the card.
I hope that this enough info for you to be able to get your triple screen rig up and running without too much difficulty and if you have any more questions I shall do my best to help you out if I can.