Best time to test water?

Does it matter when I test my water? I usually test it in the evenings.

What about testing it right before and right after my family swims, will the test results vary?

What about tests on sunny or cloudy days? Or right after it rained?

doesnt matter when you test it, just make sure the pump has been running at least 12 hours and that it isnt right after a shock

Best thing to do is pick a consistant time to test and try to stick to it. This way you will get an idea of how your pool is on a regular basis.
If you test right before and after swimming you might notice your FC has gone down slightly or that there is some CC that has formed right after if the pool has had heavy use. This is normal and will be taken care of by your next addition of sanitizer. If this is a constant problem then you might need to review your FC levels and how often you dose with chlorine. Testing right after rain will also affect your results but if there have been heavy rains once again you might need to make some adjustments to the pool water.

It is not a good idea to test right after adding chemicals. They take some time to mix through the pool. A good brushing and then letting the pump turn the water over once (Usually 4 to 6 hours) is usually sufficient for chlorine or calcium. CYA will take up to a week to dissolve so don't even test for it after adding until a week has gone by (and don't clean or backwash your filter during that time either).
Any chemicals that affect pH or TA should not really be tested for until about 24 hours or a bit longer has passed because it takes that long for the buffer system in the water to stabilize. A lot of chemistry happens in your pool when you adjust the pH or TA!

Most of your test results should stay pretty constant with the exception of chlorine and possibly pH which is why these are monitored more closely than the other parameters.
Hope this is helpful.