Good 9-speed cog configuration for touring and which low-cost quality cassettes?
First, in the front they are called chainrings, god knows why they need to have a different name, but they do.  The fronts can be sold as a set, but can just as easily be gotten individually.  I actually purchased a 26T chainring in the front for something like $10.  For chainrings you will need to know the diameter (in millimeters) of an imaginary circle that would pass through all the bolts that hold the ring on and also the number of bolts that hold it on.  Often there is one diameter that holds that smallest ring and another that holds the two larger ones.

In the rear, you don't need to know the diameter, just the number of gears.  Cassettes are often sold as a group and the two big names are SRAM and Shimano and for 9 speeds they are compatible with each other.  At the small end of the cassette, your current setup is about as small as you will find (11T), but if you are wanting more climbing ability they make big cogs up to 36T (or bigger if you want custom).  There is currently an option to go with 10 speeds but that will require replacing your entire drivetrain, not a cheap option.

Before you go replacing the chainrings, try the cassette first and see if that resolves you skipping issue.