Computer Monitor Questions

[NemoInDenial]

Im looking for a 24inch monitor, the problem I em having is my computer is like 7 years old and Im not very computer savy, anyways my question is if I put in a 24inch monitor will the computer recognize the specs for the monitor ie 1900x1200 and ect, monitor is a Samsung SyncMaster 244T.

Or do I need some graphic cards or some other accessories and if so what are they and how much em I looking to spend on these.

Thanks -Mike-