So, here's my procedure. First I make sure my cheese pot is clean (no residues or any such that might have slipped by in the last cleaning), and rinse it out with filtered water. (I have a filter at my kitchen sink to supply filtered, chlorine-free water - I use this throughout the process, but one could use distilled water instead.) I put in the utensils for the first stage of cheese making - measuring spoons, skimmer/spoon, ladle, tongs (useful for fishing things out that get dropped in, as well as later in the process), cutter, etc. The vertical cutter is just a very large cake spatula; the blade is in the pot, but the handle extends out. I put the thermometer in as deep as possible, with the head still outside. I add 2-3" of filtered water, put on the lid (it doesn't fit fully due to the thermometer and cutter sticking out, but sits as flat as possible), and set it on the stove on high. Once it comes to a full boil, with lots of steam, I turn it down a bit - enough to keep a full boil, but not wasting energy - and set a timer for 10 minutes.
In the meantime, once the pot is on the stove, I fill the sink with hot water and put the jugs of milk in to start warming. Depending on the amount of milk and the heat of the water, the milk usually reaches 70-80°F during this time, leaving very little more to do to get it warmed up to ripening temperature. Note that my hot water is not super hot, so if yours is, you may need to experiment with an appropriate temperature if you want to use this step.
Also in the meantime, I fill a small pot with filtered water and put it on the stove to bring it to boiling - this will be used for sanitizing anything that has been used, but needs to be used again. I keep this pot just at the simmer.
Also in the meantime, I use a bleach solution in a spray bottle to spray down the counter where I will keep the utensils during the process. After letting that sit for a few minutes, I wipe it dry with a paper towel - I do not rinse it, just wipe it dry. It is important to note that this is not straight bleach; according to the label on the bleach bottle, for sanitizing you use a solution that is actually quite dilute. (I'm guessing that after drying the counter, any chlorine residue essentially gasses off.) On this sterilized counter, I lay out a fresh, clean kitchen towel. The various utensils will rest on this. This begs the question of whether the towel is sanitary, and/or whether, with the towel in the middle, it matters that I have sanitized the counter. I don't know the answers, but I've been doing it this way for 110+ cheeses with no problems, so ... it ain't broke, I ain't fixin' it!
ALSO in the meantime (lots going on in this meantime!), I put ~1/4 cup of filtered water into each of two or three cups and put them in the microwave. I run the microwave on high for about 3 minutes so that the water is boiling. I use one of these to dissolve the CaCl crystals that I use to add CaCl to the milk; I put the others in the fridge to cool. They will be used for diluting annatto, rennet, etc. before they are added.
Whew! The timer has gone off, so now I empty the boiling water out of the pot and lay out my utensils on the towel, making sure that measuring spoons are dry so that the residual heat can thoroughly dry them before I use them to measure cultures. I pour my milk into the pot and put it on the stove - I have found that with my stove, I can use direct heat, carefully chosen, with equal or better results compared to using the water bath that I used to use. I add in the CaCl solution and stir it in, and gently heat the milk up to the final ripening temperature. I add the cultures, wait 5 minutes for them to melt it, then stir the cultures in well. At this point I put the lid on and let it ripen for whatever time is called for; in the meantime, I wash the skimmer/spoon or anything else that will be reused, rinsing thoroughly including a final rinse with filtered water, and put it/them in the small pot to sanitize.
When the cheesemaking is within about 30 minutes of being ready to drain the curds, I do the second stage of sanitizing. I have another large pot (though not as large as my cheesemaking pot) that I make sure is thoroughly clean and rinsed, and rinsed with filtered water. I put the cheesecloths that I will use in the bottom of this pot, and on top of that put the plastic mesh, mold(s), follower, etc. I add 3" or so of water and put this on the stove, bringing it to a boil. Over the top I drape my colander - it is way too big to fit into any pot, so I let the steam sanitize it. I have to rotate it every few minutes to be sure all of it has had a chance to steam.
A few minutes before I am ready to use all of this equipment, I use the sanitized tongs to fish out all the plastic pieces and lay them on the towel. I pour out as much water as I can, then use the tongs to squeeze the cheesecloths to expel as much more water as possible. I lay the colander over top of the towel, and use the tongs to pull out and drape the cheesecloths so that they can cool a bit. (Alternately, I may set the colander up in the sink for draining, and drape the cheesecloths there.) It is very important to spread the cloth out at least a little - hard to do with the tongs, but as much as possible - and give a couple of minutes; otherwise they will stay way too hot to handle. Once they are cool enough, I squeeze out any excess water (be careful - may still be very hot water inside the cooler exterior!). Whatever cloth will be involved in draining gets set up in the colander; others get set on the towel.
Whew! It sounds like a lot of work when I describe it like this, but really it is all very simple, and takes very little time. A few additional notes. One is that, except for the molds, follower, plastic mesh, and cheesecloth, all of my equipment and utensils are good-quality stainless steel. As long as the plastic is not resting directly against the bottom of the pot, the plastic seems to hold up just fine with the heat sanitizing. The second note is that I wash and rinse my hands thoroughly throughout the process - any time I've been away to do anything else and come back, I wash, rinse, and dry before picking up any utensils. Finally, though I use bleach to sterilize the counter, neither the cheese nor the utensils actually contact that counter - so no worries about any bleach flavor getting into the cheese.
I make absolutely no claims that any of this is the right way to do it! This is just the way I have done it, for many years now, and it has worked for me. If you adopt any of this, let us know if it does or does not work for you.