Having completed a tour with my bike (my first road bike) I can now make a few comments on it and my other equipment, and pass on some of the many tips people have generously shared with me along the way.

The Mercier Galaxy is a good first road bike, and a good touring bike for
its price. I bought mine on
bikesdirect.com for $496 and it has since been discounted to $396. The
price is right! In addition to taking mine on tours, I've also been commuting
to work on it.
The Galaxy's frame is all steel, so it's not light, but it's also nothing
that will fall apart on you.
If you are looking to buy a bike online, you do, of course, have to know
your frame size. This can be a little tricky if this is your first road bike;
I won't go into the details here.
The bike comes "mostly" assembled. All you need to complete the installation
is a set of Allen wrenches and a tube of grease— just put grease on
every metal-metal interface before you put the parts together. I put my bike
together without adult supervision in a couple of hours. (The manual is both
unhelpful and unnecessary.) Having a second person around during assembly is
helpful. The only tricky part, I would say, is getting the derailleurs
adjusted right. I don't have a good sense for visually figuring out how the
derailleurs should be positioned, so it took me a few edit/ride cycles to get
it adjusted to something usable. I imagine that if you took the bike in to a
professional (or really, anyone who knows something about bikes) they would
be able to fix this sort of thing for you in no time at all.
I installed the following parts for the tour. These were pretty quick
changes: most elements took under 30 minutes to install (first time trying).
The Galaxy is nearly ready to go on a tour.
Tires: Continental Ultra Gatorskins. Around town I'd mostly been
riding around on 25mm racing tires. For the trip, I installed the
Ultra Gatorskins, which have a Kevlar strip in them so they are more resistant to
flats (I made it through the tour with no flats). I used 28mm tires since we
were traveling loaded. The Gatorskins are heavier but having the extra peace
of mind is invaluable. In case you want to install still wider tires, the
brakes and frame do even fit 32mm tires, so you do have that flexibility.
Rear cassette: Shimano 11-34 8-speed cassette (HG40). The Galaxy
comes with an 11-30. Having that last gear be so much lower really helps on
steep grades. (With these gears, Redwood Gulch, a 21% grade at its steepest
part, turned from something I dreaded to something manageable.) Often, with a
34-tooth gear, one needs to make sure that the rear derailleur can actually
reach that far. The derailleur that comes with the Galaxy is just fine, in
fact, though I had to do a bit of fine-tuning so I could access the last
gear. You will need some more specialized tools (not just Allen wrenches) to
replace the cassette.
Brakes: Kool Stop Salmon brake pads. These brakes are nearly silent
and perform well in the rain. There's not much more to say about them! Buy
a set already.
Bike computer: Sigma BC1606L. It's light and does the job. A single
coin cell powers it for months. Additionally I borrowed a GPS unit for the
trip, but closer to home I don't usually need a GPS.
Pedals: Shimano pedals, and Shimano M086 shoes (mountain bike shoes).
I also have a matching pair of road bike shoes (R086). The mountain bike
shoes have treads on the bottom so that the cleat is partially recessed; the
road bike shoes do not, so they have a totally smooth bottom except for the
cleat. If you intend to race, then every gram matters, and you want the road
shoes. You also want the road shoes if you enjoy the feeling of being afraid
of slipping and falling on your back every time you take a step on asphalt or
tile. Maybe it makes you feel more alive. Otherwise… just start with
mountain bike shoes.
Fenders: SKS Race Blades.
I wasn't able to find fenders before I left, so I bought these in the middle
of the tour. When riding in the rain, getting a thin stripe of mud down the
middle of my back doesn't really bother me, but getting my socks wet from
the splashback can be really miserable. The SKS Race Blades are nice because
they attach with rubber straps, so they are easy to mount and unmount. (Also
important, they go behind the front fork rather than trying to fit
through it, so they actually fit on the Galaxy and other road bikes.)
Light: Planet Bike Blinky Superflash Tail Light.
(I also had a cheap no-name front light that was anemic enough that I won't
endorse it. Fortunately we didn't need to use our lights extensively.) Two
AAA batteries power the Blinky Superflash for weeks or months of commuting.
Bags: Carradice Nelson Saddlebag and Carradice Bagman Quick Release
(rear) and an Ortlieb Ultimate5 Compact (handlebars). The Ortlieb
detaches easily and has a shoulder strap, so I left my valuables (camera,
phone, passport) in there and brought it with me whenever I had to leave the
bike. Extremely convenient. The Carradice Nelson fits a shockingly large
amount of stuff, and the quick release mount is useful for commuting as well
as for touring. Both bags are waterproof.

Fully loaded bike
Update, Mar 2012: a year and a half later, this bike has seen about 4,500mi of riding on three additional tours, and I have no plans to retire it. I am still using everything on the list above except for the Sigma (I've upgraded to a Garmin Edge 800). More info about my recent tours here or here.