(1) One critical element that hasn't been emphasized in answers so far is that the microorganisms that establish your starter mostly come from the flour not the air. The idea that the creation of a starter involves "catching wild yeast from the air" is commonly repeated in many, many books and resources, but I'd be interested if anyone has ever seen a scientific paper that actually verified that airborne yeast is a significant source for establishing sourdough cultures. (I've looked a bit, and I haven't seen that. On the other hand, there is plenty of evidence for a variety of microorganisms, including local ones, in established cultures. But the primary establishing microorganisms come from mainly from the flour.)
A number of people have reported experiments to test the conditions necessary for establishing a successful starter, including ones where they tried their best to kill all starters. Sterilized containers and mixing equipment, sealed containers, and sterilized water have little impact. But sterilized flour will almost always fail to produce a viable starter. (It also makes sense that yeasts and bacteria that would like to eat grain would be likely to be found living on it at a higher concentration that floating around in the air....)
In any case, now that we've established the primary source of the microorganisms, the main goal in a new starter is to provide them with adequate food and a growth environment that will weed out other undesirable organisms. Personally, I've had the best results in beginning with a starter regime that somewhat simulates the life cycle I ultimately want for my starter. Since I generally raise dough at room temperature and expect to feed a room temperature starter roughly every 12 hours to keep it healthy, I do the same when beginning my starter.
But that's just my preference. You can get a starter going with temperatures anywhere from about 55F to 85F -- below that, and the yeast will grow way too slowly, and above that, and you're likely to grow bad stuff in the first week of a new starter. As others have said, 70-80 degrees is probably optimal for quickly establishing a starter. On the other hand, lower temperatures will tend to produce an acidic environment more quickly, which will weed out the first batch of bad bacteria. So, take your pick. As for feeding schedule, it really depends on your preferences, temperature, and hydration level. I wouldn't wait more than about 24 hours between initial feedings, but extra ones don't seem to hurt.
In terms of other conditions, you mainly just want to avoid contamination from other bad stuff, since you're encouraging growth from the flour. Thus, keep the container covered (though not sealed tight -- it can explode, which I know from experience), and out of sunlight (which encourages mold growth). Trying to "catch the yeast from the air" by placing it near an open window or something is more likely than not to contaminate the starter and cause it to fail. I haven't been overly fussy about sterilizing containers or stirring utensils, as long as they are reasonably clean. I also haven't personally had any problem using tap water from a number of different municipalities -- I know some people have said it kills starters, but it never killed mine. To be safe, use water without chemical treatments. But if you plan to use tap water in your doughs, I do believe that you want to start selecting microorganisms that won't be killed from it at the start.
Hydration varies a lot, and I've seen successes with all types of starters. Most people seem to go with about 100% hydration (equal weights of flour and water). That starts out as a thick paste and will become a little "goupy" as the days go by. Others go with higher hydration (like pancake batter), while others make a very dry dough, kneading as much flour as possible into the water, and then bury the dough in a container of flour to ferment. I haven't really seen anyone compare success rates of these various approaches, since everyone seems to have their preferred starter type, but I've found that all of them can work. If anything, the most problematic for me seems to be high hydration: they tend to grow weird stuff in the first week unless fed frequently. With a dry ball starter buried in flour and kept at a cellar temperature, you could probably feed it only a couple times a week and still be successful in getting a starter going.
That covers a lot of the "conditions" question. In sum, a wide range of conditions can work -- just avoid contamination and keep out of the sun. Feed on a regular basis. Don't throw any random stuff in your starter (milk, sugar, grapes, potatoes, beer, whatever) -- in most cases, it is more likely to hurt through contamination rather than help. (See the note about acids below, however...)
Moving on to the other questions:
(2) Whole grain flours work best, since they have a greater number of microorganisms than white flours. I've had greater success with rye, which has different sugars than wheat, but I know other people who swear by whole wheat. I've had a few starters with white flour fail, though, so I've given up trying to start that way. I'd suggest if you want a white flour starter, establish it with whole grains first, and then transition it to feedings with white flour after a couple weeks.
(3) Acidic ingredients can help a starter in the first 3 days or so. Basically, most starters go through a phase after about 2-3 days where you'll see very rapid growth. Don't get hopeful -- that is rarely due to good yeast. Instead, experiments have shown that it is due to a bad bacteria, and unless it is weeded out of your starter, it can prevent the good yeasts and bacteria from getting established.
Luckily, the bad bacteria produce waste products that tend to acidify the starter anyway, and eventually they will acidify it enough so that they can't grow anymore. Sourdough yeast and bacteria are selected to live in acidic conditions (hence, "sour" dough), so they will eventually take over.
Nevertheless, you can help out this weeding out process by giving an acidic boost early on. The simplest way to do this is built into many recipes. Instead of doing a typical sourdough feeding where you double or triple the weight of the starter, many recipes suggest only feeding the same amount for the first 3-4 days of a new starter. So, if you start with 10 units of flour and 10 units of water, you just keeping adding 10 units of each at each feeding. By the fourth or fifth feeding, you're only going to be adding a small amount of new food compared to the overall size of the starter. That will still help the yeast grow, but it will concentrate the acid produced in the starter so far and stop the bad bacteria from establishing itself.
(Note: You don't need a lot of flour to get things going. Even a small amount has a huge amount of microorganisms ready to grow. I usually start with a tiny amount, say 10 grams each of flour and water, and then feed 10 grams each with each feeding. Don't throw any away. After a few days to a week, you'll often be ready to bake your first loaf, and you don't end up wasting any ingredients.)
A number of online experimenters have tried using other acidic components at the outset, and the easiest option does seem to be pineapple juice used in place of water in at least the initial feeding. Orange juice and apple cider can also work if used in the feedings for the first few days. Other acids (e.g., vinegar, lemon juice) can work, but it's harder to get the "dose" right. The most effective seems to be a dose of ascorbic acid powder added at the outset, but most people don't have that on hand. (Don't try crushing vitamin C tablets -- they usually have buffers that will negate the acid effect.)
Personally, I find feeding once every 12 hours for the first few days (as opposed to every 24 as recommended by many recipes) and keeping the feeding amount the same, but not throwing any away for the beginning is sufficient to overcome the bad bacteria. The fruit juice can also add contaminants, so I don't usually use it, but it appears to improve your chances significantly if you use widely spaced feeding schedules or higher hydrations.
By the way -- note that the acid will only get you over the first hump. In most cases, it will take a week or two before you've really weeded out most of the bad stuff from your starter for good. Keep up the regular feedings.
(4) Milk and sugar. Just don't do it. Milk can provide a slight acidity as it sours, but it's more likely to bring in bad bacteria or grow mold than the fruit juice option mentioned above. Sugar helps a lot of microorganisms grow, but at the beginning of a starter, it's more likely to grow bad bacteria than good yeast. I know some people add sugar to a mature starter with each feeding, but it's not necessary. I don't have a lot of experience with this, but anecdotally I've heard that it can throw off the "rhythm" of yeast and bacteria growth even in a mature starter, effectively reducing the rising potential of your starter.
Sometimes with a mature starter, you should add milk and/or sugar as part of the recipe to build the final dough. That will depend on the type of bread. But I never use either in regular feedings.