For me, there are only 2 kinds as far as the results I've seen - Live and dead. Live is good. Dead not so much.
Actually I have used 2 kinds - instant or quick yeast, aimed at the inflexible time frame of the bread machine; and active, which is what I use for pretty much everything including bread machine recipes. I don't use the packets because many of the breads I've made don't call for using that much yeast. Each packet is 2˝ teaspoons, and recipes like my ciabatta only call for 1˝ teaspoons for 3 loaves. What do I do with the leftover teaspoon? With the jar, I just measure out what I need.
Regular active yeast work seems fine without proofing it, but I usually do that anyway for insurance. It only takes 5 to 10 minutes to proof your yeast in a cup or less of warm (about 110°F) water. You can feed the yeast by adding 1/2 tsp of sugar to it if you like - that won't change the taste or texture of your bread - but it seems to be about the same whether I add sugar or not. The yeast and water still get sort of creamy looking and that tells me that the yeast is doing okay.
I keep my jar of Red Star in the freezer to help it last longer. I've had a jar for as long as 1˝ years still going strong. Using water that is too hot, or too much salt before the rise, can kill your yeast too.