First things... You make mead and brew beer.
Now then, I think the honey and water mix has been addressed already. So not going to go over that again. The sediments you get on the bottom of a fermenter, from the yeast, is not really all that good for using in another batch. MAYBE, if your first batch was a log OG, it fermented to dry, and the yeast has plenty of vitality left (you hit 7% on yeast rated to 14%) you could use it again. But I don't know of anyone making mead that wimpy.
Most of us select a yeast, or formulate the must, to maximize the yeast used. So, formulate it to hit 14%, finish a little north of 1.000, and used D47 yeast (for example).
Do yourself a big favor, get yeast nutrients made for making wines. Such as Fermax, Fermaid-k, DAP and also yeast energizer. Fermax and yeast energizer have a per gallon dosage on the containers. I would advise using that for your first batch. Give it all while mixing up the must and then add the yeast (properly rehydrated).
It's important to remember mead takes TIME to become something great. Where you can go grain to glass, with beer, in a matter of weeks mead will take significantly longer. Several months if not over a year (depends on how strong you're making it). You'll also rack the mead at least a few times during the process, but don't do this too often. Wait until it's completely finished fermenting before you rack the first time. Then give it 1-3 months, and allow it to clear, before racking again. I've racked a couple of more times on top of that, depending on the batch and how it looked.
If your mead ferments to dry, read up about back sweetening. Just keep in mind that you want to aim for less than what you're sweetness target is in this case. Where it might taste perfect once you're back sweetened and then bottle (either stabilize, or give it enough time to ensure fermentation doesn't pick up again) it very well could come out tasting too sweet a year (or several) later. To the point where you don't want to drink what you have left.
For your first mead batch, I would go with a traditional formula. Basically honey with a strong flavor to it (that you love), water, nutrients, and yeast. I (and many other mazers) use
Lalvin yeast strains for our meads. I would select one of those that appeals to you, or you can keep it in the temperature range listed while fermenting. At your initial formulation, you should be able to get to 14%, so D47 would be a solid choice. I wouldn't suggest using 71B for a first batch since it is a more needy yeast, and needs some different treatments.
I would also suggest going over to the Got Mead forums and checking out the information there...
Above all else, do NOT heat the honey/must above 100-110F while you're making it. If you do, you'll start to lose the more delicate flavors and aromas that are present in the honey. Since you're going to spend decent money on the honey, don't do that.
