So, I turn to here for advice and knowledge, as I am in the midst of this restoration of a frame that I love.

I bought it in Brooklyn, NYC in about 1996, in ride-able condition from my landlord for $100. Its about a 52-53 size Bianchi in a fire engine red with chromed tips, meaning that the drop out ends of the stays are chrome and so is the lower half of the front fork. The rest is red, well, it was before the chips and rust set it. As much as I want to keep it real as is, I have determined that the paint and chrome are so far gone that it all needs a respray. But the story continues...

In about 2000, I had the bike converted from gears to a freewheel single speed by a reputable shop. I was helped by a young guru who outfitted the bike to be 'bombproof' as well as a fun, lightweight single. The original suntour components were removed and a new BB was put in place, as well as a strong, but cheap wheelset of mid quality stuff. I was poor and needed the bike to just function. I kept the brakes and drops on.

I sold the bike in that condition to a friend in about 2005. I bought it back from him on 9/14, and had the bike shipped from Texas to Md. It was not treated that well. Some stuff will just be replaced, other components might be worth holding on to. This is where I need the help in determining what will fit, and what it worth refurbishing.

I need a new wheelset, period. The dropout distance I measure as 128mm, made for gears, of course. The BB is 68mm wide, making it English, and I have removed the cups and caged ball bearings and the spindle, which appears to be a newer Shimano unit, which is 120mm in length. I would prefer to use a sealed cartridge unit, can I use the same spindle? I am looking at these wheels:
VELOCITY DEEP V BLACK SHIMANO ULTEGRA 6800 HUBS 9 10 11 SPD 36H
I am pretty sure it is a good fit, but wanted to run the specs past y'all to ask for your opinion.

My crank arms are SR Apex Japanese and are 170mm in length, with a single small chain ring on it. I count 39 teeth, but I am counting from a photo, so I will confirm the gearing and the cog teeth. They seem to be in fine condition.

I have a front pull brake on bullhorns up at the stem, but I am in need of the reverse pull handle for it, so that it sits on the end of the right side horn. I do not plan on using a rear brake, as my speeds and distances are very low.

My new paint scheme is looking like a silver metallic for the tubes, with deep metallic red for the lugs.
I have filed off the extra items on the frame like the cable hangers and the shifter mounts, in preparation for the painter. I am going for a minimal look, with the all black wheels.

The seat post and seat are toast, both are just corroded. I will need new, something sleek.

My stem and headset stuff looks to be fine, but I would like to hear advice. Perhaps I need more dimensions to really get down to brass tacks. Right now, its a basic setup.

I am going to use this bike for travel between buildings at work, about 1/2 a mile. It will be stored indoors. It will be more about its aesthetics than anything. It doesn't have to be super comfy for long distance, nor rigid or lightweight for racing. I have the money to make it great, but I don't want to just throw dollars at it insanely. I will hold on to it forever, this is just another chapter in its life. Perhaps when I am old it can be revised into something else for use.