You've got some good advice here. If you can find a touring bike with a triple crank in your size, go for it. Otherwise, an '80s Japanese road bike with a double in front and the biggest low gear you can put on the back (32, if you can swing it). You'll learn what geometry works for you, but I'd look out for relatively long chainstays and long wheelbase -- not a twitchy racing bike.

As for tires: I'm not convinced of the need for very wide ones. I find 28mm (27 x 1 1/4) ideal for the distances you're riding.

As you ride, you'll figure out what's comfortable (or not) for you -- it's very personal. But I'd say that many people don't do well with vintage drop bars. I prefer bars where the drops are parallel to the ramps; your preference may vary. You might also prefer something like moustache bars. The Nittos are excellent.

As for saddles -- again, it's personal, but most people do like a Brooks. Look out for deals on eBay -- or just make an investment in a Brooks Imperial.

For U-locks, I've done well with both OnGuard and Kryptonite. The important thing is to use it -- and if you can help it, don't leave it locked up outside overnight.