Well, without knowing your budget..........it would be pissing in the wind to suggest anything at all.
Since you have 3 monitors that you want to run....you would most likely be better off just building your own.
Keep in mind that just because a video card or MB has 3 video outputs does NOT mean it will drive/run 3 displays at the same time.
If you do not plan on gaming, just so long as your OLD video card is NOT an AGP card you can use it your new system so long as the MB has another PCI Express 16 slot and the Power Supply is large enough to power it.
If the computer has onboard integrated graphics they usually support 2 monitors and if you have an open PCI Express 16 slot you can either buy a discrete graphics card or use your old card. Again, provided the PSU can handle it.
Just keep in mind that if you try to use Onboard and Discrete graphics at the same time "some" MB BIOS will NOT let you use both, while others will.
You just have to do some tweeking to get them to work together. But Windows 7 will run your monitors just fine from any video source so long as the BIOS or UEFI supports it.
Just an FYI........Your Power Supply is the most critical part of your computer. Most OEM systems use CHEAP PSUs. This is why I always build my own systems.
The second most important part is your Motherboard followed by your graphics card and RAM. Then your CPU and CPU Cooling. (Fan Or Water. I prefer Fan cooling with Arctic Freeze MX-2 non-metalic thermal paste.)
Then your computer case. As in Air Flow, Accessibility, and Durability.
Then an SSD drive for the OS and nothing smaller than 240 GB. The Samsung EVO's are great drives for price, speed, capacity and reliability.
If the computer is for your business, I would suggest getting an Enterprise HDD for the data storage. WD RE4 or SG Constellation. (But do NOT get them from Newegg or independent sellers at Amazon since most of these drives are OEM and do NOT have the 5 year warranty that they say they do.)
Though Enterprise drives are made for RAID setups, they work just fine as single drives and are much more reliable and last longer.
In the last 8 months I've built a Xeon Workstation for around $2,500 that runs 3 monitors and a 50" TV and an AMD 8320 for around $1,200 that runs 2 monitors and another 50" TV. Both systems have 32 GB of ECC RAM. RE4 and Constellation HDD's and a Corsair Neutron GTX 480 GB SSD and Intel 320 240 GB SSD.
The Xeon has a SeaSonic Platinum 1050 Watt PSU and the AMD has a Corsair HX 750 Watt Gold PSU. My Old Backup 4 core AMD system has a SeaSonic Platinum 650 watt PSU in it.
So, throw out a number for your budget and whether you're comfortable building your own system or you're set on getting an OEM system and I'll see about offering some helpful advice for you.