I'll try to answer the original question. None. I would not trust any cheap thermometer and or hygrometer. The best least expensive thermometer I have encountered is the herpstat at 100$ for a +/-0.5ºF is actually quite a fair price. (unless you can deal with liquid crystal ones)
OK so lets move to realities. Few are willing to spend 100 + for a thermometer. Accurate hygrometers are so sensitive to dirt and dust that you wouldn't use one even if you have one. IR guns are about the same specs as all the rest +/-2º where in the 4 degree range is variable they also reflect off shiny objects so they must be used intelligently.
The best answer I have is buy a few of the same model and lay them out and compare them against each other. (5 is better than 3 but 3 will work) Typically two or three will read close to the same they are likely more accurate than the others. Almost all the sub 100 mark are the same specs +/-2º so by using a majority rules you can eliminate ones that are reading wrongly. I usually buy the cheapest (2-6$) I can and ten or more and mark the good ones and give away the bad ones.
Hygrometers are easily checked with a salt test (google salt test humidor) and choose one. It is easy and will get you to within 2% accuracy good enough. Personally I like ones that can be calibrated the little tags saying -16% and +32% bug me. I have a digital one but the calibration dial is easy to move and on the front. Sometimes my snakes take a turn calibrating it. I have abandoned it and gone with a cheap analogue calibratable model they hold accuracy for about 10 months or so. I check them every 6 because I am a spaz most would be ok with every 12.
Using a fogger is one solution to humidity, I have never done so my self but I see no reason why not. The only issue I have with it is it needs to be cleaned frequently (like every time you add water to it) ultrasonic ones are bad for bacteria so keeping on top of it is a good idea.