My girlfriend and I make 12-15 batches of mead every year, mostly melomels from seasonal fruit. She has been doing this since the mid nineties and over the years she has learned what isn't necessary. We don't use yeast nutrients or Camden tablets and have done hundreds of batches with no fermentation problems. we also don't use any finings and get a clear product. I think the most important thing is to be patient: 10 days to 2 weeks in the primary, stirring everyday, rack to carboys filled up into the bottom of the neck and leave at a fairly warm temperature (70ish) for 4-6 months (if its at the longer end we will rack off the lees after about 4 months) then rack into new carboys and put in a cool place (our cellar is usually 55-60) for at least 6 months but longer if you can stand it. We usually bottle about 1 1/2 years after starting. I think the long secondary fermentation and aerating everyday during the first is why we don't need yeast nutrient. I can't recall a stalled fermentation. As far as sulfites go mead doesn't seem very susceptible to infection and to me getting a product with no sulfites is one reason we make our own. We do put a Camden tablet in the water we soak our corks in to prevent the corks from getting moldy/infected. We have also found that by racking a couple times and aging a long enough time the mead almost always comes out clear.
A couple more pieces of equipment: a stand up corker, corks, and bottles, something to prevent light from getting to the carboys if you don't have a constantly dark place (we use pillowcases with a hole cut for the airlock), and mesh bags for holding fruit in the primary. Also, if your using fruit and bring to a boil or use boiling water to steep it in, pectic enzyme.