There's a lot of misconception about what will and will not work with LabView and what you do and do not need to build a decent system with it.
First off, as others have said, test and measurement is expensive. Regardless of what you end up doing, the system you describe IS going to cost thousands to build.
Second, you don't NEED to use NI hardware with LabView. For thermocouples your best bet is to look into multichannel or multiple single-channel thermocouple units - something that reads from a thermocouple and outputs to something like RS-232, etc. The OMEGABUS Digital Transmitters are an example, but many others exist.
In this way, you need only a breakout card with lots of RS-232 ports and you can grow your system as it needs it. You can still use labview to acquire the data via RS-232 and then display, log, process, etc, it however you like.
Third party signal generators would also work, for example. You can pick up good ones (with GPIB connection) reasonably cheaply and with a GPIB board can integrate it into LabView as well. This if you want something like a function generator, of course (duty cycled pulses, standard sine/triangle/ramp functions, etc). If you're talking about arbitrary signal generation then this remains a reasonably expensive thing to do (if $5000 is our goalpost for "expensive").
This also hinges on what you're needing the signal generation for - if you're thinking for control signals then, again, there may be cheaper and more robust opitons available. For temperature control, for example, separate hardware PID controllers are probably the best bet. This also takes care of your thermocouple problem since PID controllers will typically accept thermocouple inputs as well. In this way you only need one interface (RS-232, for example) to the external PID controller and you have total access in LabView to temperature readings as well as the ability to control setpoints and PID parameters in one unit.
Perhaps if you could elaborate on not just the system components as you've planned them at present, but the ultimaty system functionality, it may be easier to suggest alternatives - not simply alternative hardware, but alternative system design altogether.
edit :
Have a look at Omega CNi8C22-C24 and CNiS8C24-C24 units -> these are temperature and strain DIN PID units which will take inputs from your thermocouples and strain gauges, process the inputs into proper measurements, and communicate with LabView (or anything else) via RS-232.