I had the same questions when putting together my 1986 Trek 310 Elance.

My bike was free, and a total basket case. The cranks and bottom bracket were the only usable parts on it, everything else was completely shot.

I built mine up 3 years ago, I went with a complete Shimano 105 (5800) 11 speed groupset and Ultegra Hollowtech II bottom bracket - from Pro Bike Kit

The wheels are Mavic Open Pro 32 spoke 700C rims with DT Swiss spokes and Shimano 105 (5800) hubs - from Velomine

Based on recommendations here, I went with Panaracer Pasela 28mm tires - from Bike Tires Direct. They're fantastic.

With the conversion to 700c wheels, I also needed to mount a set of Tektro 539 dual pivot caliper brakes. I needed the 53mm of reach. They were from Amazon.

Other parts you'll need include cable stops and possibly a clamp-on adapter for the front derailleur

Everything went together very easily, the only sticking point was you need to take your time and be VERY patient when mounting and dialing in the front derailleur.

The brifters just work. Smooth, efforltess, predictable. Also, if you're on vacation with the bike and need a repair, most any shop is going to have the parts, tools, and skills needed to work on newer Shimano stuff.