See Sections 2.5 and 2.6 of the U3 User's Guide. The U3-LV has 16 flexible inputs that can be digital input, digital output, timers (2 max), counters (2 max), or low-voltage (0-3.6V max) analog inputs. The difference with the -HV compared to -LV is that the first 4 flexible inputs are changed to fixed +/-10V analog inputs. From what you have described about your application, you just need 1 or 2 timers to create output pulses, so you can use the LV or HV. Most people buy the HV because it has the +/-10V inputs and still has 12 flexible I/O.
As for other devices from LabJack, the U6 would be a USB-only device with higher quality analog inputs. The T7 has the same high-quality analog inputs, and provides USB, Ethernet, and even WiF on the -Pro version.
