You've read a lot of stories about making yogurt. I think there are enough innovations here to give you something new and interesting. If you need a gallon of yogurt every week, this is the fastest, most reliable, easiest, and cheapest home process by far. I'll have further musings at the end, but let's get right to it.
You will need a gallon of milk in a plastic jug, a pot bigger than that jug, 2 coffee filters, 2 oz. of plain yogurt in a cup-sized jar, a pair of gallon-sized shallow food containers, an insulated container to hold the jug, a drill or sharp knife, a cooking thermometer, and a kitchen with a stove, fridge, and sink.
The cheat sheet.
1. Sanitize everything.
2. Heat to 180 - 190F.
3. Cool to 100 - 110F.
5. Ferment for 6 - 24 hours.
6. Strain in refrigerator.
Step 1: Scald the milk to 180º - 190º
Poke the temperature probe through the cap. Reserve a cup or two or three for pudding and place the jug in the pot. Add just enough tap water to barely float the jug. Cover the pot if you can and set the burner to high.
It takes my electric stove about 25 minutes to heat the milk to 175F. Then turn off the heat and let it coast up to 180+. I use a timer so I can turn my attention to other things, but depend on the thermometer.
It's hard to find the perfect vessel for this, but it really doesn't matter to the yogurt. Mine is a 12 quart aluminum pot, over 10 inches high inside, with a glass lid that has a vent hole. It saves time and heat. You can do this in an open 3 quart pot for a trial run, but it's more trouble.