I am not familiar with using nvidia surround but a quick search says that your motherboard needs to be sli compatible, unless you have the gtx 295, 590 or 690.
Unless you are referring the the 3D surround which would require 3d compatible monitors.
As for using 3 monitors it really is up to you, I have to 660ti and have 2 hooked up to dvi ports then the third (a tv) to the hdmi port. What size monitors are you looking for? By watching sales I have found 23" monitors in that range. Microcenter.com and newegg.com both have them for around $130
On the nvidia website it said that with the 680 you can have up to 4 monitors with 3 setup in nvidia surround and 1 as an auxiliary monitor. But I don't know if i need a monitor with a display port on it or not because with previous cards you need sli and HAD to use a display port. But nvidia confused me.
I use a 670 with 4 monitors. The 3 monitors in surround use DVI (I use an active DP adapter on one of them) and then a 4th on hdmi.
So yes you have to use the displayport port, but you can use an adapter.
I have mine setup with a displayPort and two DVI in surround and my forth monitor using HDMI. But to tell the truth I never tried hooking up 3 of my monitors without DisplayPort since all of my Asus 27" monitors support it so I can't really say if it would have worked without one of them being on DisplayPort or not. This setup worked correctly for Windows 8 and Hackintosh 10.8.2 so I have not messed with it.