The whole BP/W stuff is so modular that it can seem a little DIY (even though it isn't). And there are also many very good brands and products to select from.
Tobin (Deep Sea Supply aka DSS) sells a complete kit that works out of the box (what he listed plus, perhaps, a DIR knife). I like (and own) some of his stuff. You can make it easy on yourself and just call him or read on...
So here is what I would include in my list if you are diving a single tank:
Backplate -- Lots of choices in sizes and materials. A SS plate is sturdy and takes weight off the belt. An aluminum or kydex plate is lighter for travel.
Two Cam Bands -- Needed to attach the tank to the plate. Something like the wedge blocks are also darn handy.
Harness -- You can do something like a simple HOG or one of the comfort harnesses. A hog harness consists of one long piece of two inch resin impregnated webbing, a weight belt buckle, some d rings and some tri-glides. Often sold in a single kit.
Crotch Strap -- These are important and not nearly as problematic or uncomfortable as one might think. You want the softer webbing for this area
Wing -- Lots of choices. Most (all?) come with a lp inflator hose. The trick here is to get the right wing for the right job. Don't get a wing that is designed for both singles and doubles -- if you dive singles now, get a singles wing now.
Odds & Ends -- I like a couple of marine grade bolt snaps, some cave line and a few extra tri-glides. Perhaps a DIR knife. The bolt snaps I use to attach things like my pressure guage, octo holder or dive lights to a d-ring. I often get the single ended bolt snaps so I use cave line to attached the SPG or an oct holder to the bolt snap. The extra tri-glides I use to hold anything I keep on my waist band in place. Depending on the plate, you also use them to keep the harness from moving (not needed on a DSS plate).
Here are some other possible considerations:
a) Do you need a single tank adapter (STA)? I don't need one with my DSS set up but other wings do require them.
b) Do you need sex bolts? I don't need any with my DSS set up but some wings do require them (to help attach the wing to the plate).
c) Other stuff. The key here is to get only what you need and avoid adding too many things you don't really need.
Like what? I went with a hog harness and found no need for the extra padding (back plate plate, shoulder pads) that is sold. I was also fine without all of the extra things in a comfort harness such as quick releases. You do need to figure out pockets -- lots of choices. You can use a pair of x-shorts or glue pockets onto an exposure suit. I went with a zippered pocket from dive rite on my waist belt. (Holds a sausage, mirror, Ikelite pca, mask defog). For additional weights, I use a DUI Classic Weight & Trim Harness.
