Hey man, love Civ V! Love to play a round with you sometime.
Now to the question.
Civ V can actually take some heft to play on higher settings, so the 7770 seems like a decent choice for mostly medium settings (maybe some high settings on certain games). Not a bad start, especially at that price!
I'm not sure what you've got in the terms of OS or software already, so I'll just do a full build for you
Case: COOLER MASTER HAF series RC-912-KKN1 Black SECC/ ABS Plastic ATX Mid Tower Computer Case (it's the one I use. Reliable and cheap. good chioce for a first build)
CPU: Intel Core i5-4430 Haswell 3.0GHz LGA 1150 84W Quad-Core Desktop Processor Intel HD Graphics BX80646I54430 (A great chipset, but there's a great article here on Tom's that can help you look for the right CPU for you)
Motherboard: GIGABYTE GA-H77M-D3H LGA 1155 Intel H77 HDMI SATA 6Gb/s USB 3.0 Micro ATX Intel Motherboard (Pretty basic mobo, again good for first build)
Power supply: CORSAIR Builder Series CX500 500W ATX12V v2.3 80 PLUS BRONZE Certified Active PFC Power Supply
RAM: G.SKILL Ripjaws Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 1066 (PC3 8500) Desktop Memory Model F3-8500CL7D-8GBRL
Hard Drive: Seagate Barracuda ST1500DM003 1.5TB 7200 RPM 64MB Cache SATA 6.0Gb/s 3.5" Internal Hard Drive
DVD/Disk Drive: LITE-ON DVD Burner - Bulk 24X DVD+R 8X DVD+RW 12X DVD+R DL 24X DVD-R 6X DVD-RW 16X DVD-ROM 48X CD-R 32X CD-RW 48X CD-ROM Black SATA Model iHAS124-04 - OEM
Networking: Rosewill N900PCE Wireless N Dual Band Adapter IEEE 802.11a/b/g/n PCI Express Up to 450Mbps Wireless Data Rates Support 64/128 bit WEP, WPA-PSK/WPA2-PSK, 802.1X
OS: Windows 7 Professional 64-bit
Total Cost : $709.82
Part List:
http://pcpartpicker.com/p/1C8QX
I think that's all you'll need for a good starter build
Hope this helps man, and hope you enjoy your rig when it's done!!!