I'm evaluating how to best match a new handset and rear wheel to a vintage rebuild My first bike after  move to Japan. Picked up an old 520 Cro-MO frame by Tsunoda - Grand Prix , minimal rust and decent paint. It had some old Suntour VX derailleurs, aluminum-far-too-narrow drop bar with suicide brakes, Sugino 165 cranks, lowbar Shimano friction shifters, Araya 27x1.25 aluminum rims (close to true) and a freewheel 6 speed -Suntour  -  125mm rear end.

I decided for now to go with the original wheels (new tires, tape and tubes - repack bearings &amp; replace rear axle), but swap the old freewheel for a new  Shimano 7. front derailleur to Sora double, rear derailleur to Tiagra  RD-4601 (10 speed), keep friction shift for now, replace handlebar, breaks Tektro Long.  

So here is the part that I am very interested in hearing from people about; I wanted to work with the bike for a while, get a good feel before settling on a handset (this will be the biggest cost and from what I can tell the most constrained decision)which includes deciding to change wheels or build a new rear 27 to go with modern 10 speed index shift or get a handset to work with the 7 speed or what?
Tsunoda are/were a mass manufacturer in Japan somewhat similar to Schwinn in the USA. Most of the bikes they produced were low end though they did make some mid-to-upper end models (I once had a Tsunoda made Lotus branded frame from the early 80s). I believe the brand is still around in the Japanese market but now mostly making folding bikes. Your bike sounds like a mid-range bike based on the SunTour parts. It's a very nice sport-touring bike. It's nothing special though arguably better made than comparable bikes of today. In their day the Japanese made mid-range bikes were almost always better built than comparably priced European bikes and often better built than many high-end European bikes! Japan still make amazing bikes though exchange rates keep them from being exported the way they used to be. 

The rear end is 126mm, not 125. 126mm was the standard up until the late 80s when 8 speed cassettes were introduced. The 126 spacing, VX derailleur and SunTour 6 speed freewheel likely dates your bike to the late 70s to mid 80s. The 27" rims while rare in most of the world by this time were still very common in Japan. 

Not sure what you mean by "handset". Are you talking about the STI brake levers that also act as shift levers? I'm assuming you are since those are now the norm. If so, there are a few things to consider:


You will need to respace the rear end of the frame to 130mm. This should be done by a bike shop and even better by a frame builder. 10 speed cassettes and modern hubs are spaced to fit 130mm frames. It's not an expensive or difficult process but does take a certain degree of skill and specialized tools. 
Yes, you would need to build a new wheel to convert to 10 speed. Your wheel uses a freewheel hub. This means the cassette cluster also houses the freewheel/clutch mechanism. Modern 10 speed drivetrains use a cassette hub in which the freewheel/clutch mechanism is part of the hub and the gear cluster simply slides onto the hub. You can still find 27" rims, especially in Japan. Unless the rims are very worn out I'd probably stick with the original rims and just change the spokes/hub. Panaracer still make some nice 27" tires. 
Ideally, you would also replace the chainrings. Modern 10 speed drivetrains really work best with the special chainrings designed for them. These rings have cut away teeth, pins and ramps designed to help the chain move smoothly from one ring to other (especially from small to large). You can often buy a crankset with rings for not much more than just the rings themselves. 
You will need a new chain. 10 speed drivetrains require a much narrower chain. 


One last note: the 27" Araya rims you mention are almost certainly a hookless design. Most rims have a small lip design to help hold the tire on when it's inflated to high pressures. These rims almost certainly do not. I would advise against inflating the tires past 75 psi/5.2 bar.