Well the key thing is to have some way to periodically check your probes and calibrate them. This means that you need a single really accurate temperature monitoring device for cross calibration, a device specifically designed to standardize/recalibrate, or you need to budget for getting them professionally calibrated periodically. I honestly don't have a ton of experience with thermocouples but have been told before that linearity is a concern. It isn't like a thermistor where there's usually just an offset when they are calibrated, right? They work through Seeback effect and the equation is much more complicated.
On a budget, I suspect that something like a Fluke 2190 (get the multiplexer and you can have LOTS of probes) and type Ts is about as good as you can do.
For price/performance on temp monitoring, do not forget that being able to dump the readings to a PC is worth some money. I have analog temp readers now and it is a hassle.
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