My motherboard is a 945GCT-M2/1333 (V1.0A). It only has one PCI-E slot and integrated Intel® Graphics (GMA950) (it's bad, but in no way I want worse). The CPU is Intel® Celeron E1200 and the PC has 2GB RAM.
I've got two VGA monitors, one is currently hooked up to the PC, but I also wish to use the second one. But I could get a used DVI monitor, but that would probably cost me a bit too much in addition to the graphics card so I'd seriously rather not.
Basically any video card that can handle two monitors at 1280x1024 and won't bottleneck the system overall would do. But it has to work under Ubuntu 15.10 64bit properly.
I'll repeat for clarity that there are two VGA displays, the motherboard only supports PCI Express x16 v1.1, it can not be a downgrade and it has to be supported well under Ubuntu 15.10. That means only a small range of cards is left.