Hello,
If you are trying to do Real Time Control, National Instruments has LabVIEW Real Time that you can use with one of the Real Time Modules such as FieldPoint. Check out the Compact FieldPoint controller for more information: http://sine.ni.com/apps/we/nioc.vp?cid=13446〈=US
However, if you want to use your 6110 board, I would advise LabVIEW because it integrates very well with Hardware and is very easy to program since it is graphical. LabWindows integrates with hardware as well and would be a good fit if you are a text based programming fan.
Regarding your last question, any board can work with LabVIEW. However, the board manufacturer will need to develop the driver for the board and make sure that the driver integrates very well with LabVIEW. In other words, you could not use NI-DAQmx with a board from a different company.
Hope it helps.