Any advice on a high quality set of files appropriate for gunsmithing?

For wha it's worth, I generally buy this type of thing from Brownells.

Thanks.

Brownell's is the place to buy.

You can also find gunsmith size Swiss files from jeweler's supply houses, especially higher grade needle files.
There are several who sell online.

Files are something you really don't buy "sets" of.  You buy a few of the size, cut, and type you need and then add to that later as you need them.
One of the handiest types is the "Hand" file.  This is parallel on both sides and in thickness.  In other words there is no taper.
One side is a safe, no-cut side.
These come in sizes from around 3 inches up to over 12 inches or more, and in many cuts.

Interestingly, there is a company in California that "sharpens" used files to cut like new.
This is very economical, much cheaper then buying new files.

Boggs

Very interesting, thanks for all the info.

What is the purpose of having only one cutting side on a hand file?  Is this generally a more "precise" file?

Also, I actually thought that hand files were available in many different profiles, not just rectangular.

By the way, the first job will be fitting a 1911 safety.

The "safe" edge allows cutting one surface without cutting another.
If you need to file a surface close to a vertical surface, the safe edge will allow cutting the one surface and not the other.
As example suppose you need to file the bottom of an "L" shape but not the vertical part.
By putting the safe edge against the upright of the shape, you can cut the bottom but not the upright portion.
The safe edge simply allows protecting one surface that you don't want to file.

A standard safe edge file will have cutting surfaces on both sides but only one edge.
Many files of various types will have safe edges.
Sometimes it's possible to make a special purpose safe edge on a file by grinding the cutting surface smooth so it won't cut.

I have several triangular Swiss needle files I ground off one of the three sides to make a safe edge.  I used to use these to file dovetail cuts.
For instance, if I needed to widen a dovetail but not deepen it, I would put the non-cutting safe edge down on the bottom of the dovetail, with a cutting edge against the side.
This would cut the dovetail wider, but not cut the bottom.

Get some file stones also.
They leave a much smoother surface.