Watch for evidence of flair, and try to make sure the light is even.
Do yourself a favor and try LODIMA paper and follow Michael A. Smith's advice on development. You will never see a better silver print.
Any book on photography printed prior to about 1980 will provide good concise instructions and information about materials.
A point to remember - Enlarging paper are many times faster than contact papers and very quickly overexposed with an ordinary light bulb. A 7 1/2 watt bulb at 4 feet covered with several layers of toilet tissue provides plenty of light for enlarging papers.
I realise that availability might be a problem over in USA, but Foma make a perfectly adequate (even rather nice actually) contact-speed, silver-chloride, double-weight paper. The name of the product is Fomalux and is available, in Europe at least, in a wide range of sizes.
Fomalux can help in the process of making a contact-print as it is a lot slower than normal enlarging paper, ISO-P 12 versus ISO-P 110 for the equivalent Ilford Galerie paper, making the traditional hanging light-bulb printing method more practical and has a very 'traditional' appearance. It is a fibre-based paper, rather than RC, so if the OP can obtain some of the paper, he might also want to find some washaid to make the washing more quick and efficient.
Just as a point of information, it used to be possible to obtain Fomalux in RC, though hard to track down (I got some through the good offices of an APUG member from the Czech Republic); it doesn't appear on Foma's website, so perhaps they have stopped making it
I am now sure for which reasons you want to do a contact print; is it for proofing your negatives or just getting an overview of your images? If your main goal is proofing, check out the link provided at the end of this post.
As Mr. Halfhill writes in his article, you should expose your paper until your blacks are black, not less and not more. You do test strips to not to find a workable exposure for most of your negatives, but to find out when the most transparent part of your negative (the "whitest" part) becomes black on your print.
If you "standardize" your process this way, all of your proof sheets can be compared. Plus, you get some information as to whether you will need to burn or dodge your print excessively, or whether all tones of gray will simply pop out of the developer.
Both surfaces of your enlarger lens attract dust and other grut. In a perfect world, the surfaces are pristine. In my world, they attract a lot of dust and even a fingerprint. Normally this isn't an issue because you set the focal plane to that of the negative behind the lens. You can (if you are not careful) set the focal plan to another point... such as the surface of the lens itself. When you do that, you project a very very sharp image of the grut on your lens. I had forgotten that.
The other night, I was printing a very pristine 8x10 that I had methodically cleaned of dust. The contact frame glass was pristine too. And yet, my print came out horribly. The sky was cluttered with white spots and there was a giant fingerprint in the sky. WTF? I asked myself. Before the forehead slap moment, I went back and minutely examined the frame glass and the negative again. They were still spotless. Then it hit me like a sack of wet cement. Enlarged fingerprint? That can only have come from the light source.
I examined the lens and sure enough, it was filthy. After a thorough cleaning, I printed again. Better, but not great. Now there was only one big bright white spot. Again, the lens wasn't pristine but was as close as I could get it. I took a clean white piece of cardboard and held it under the enlarger light. The projected grut was clearly and sharply visible. I unfocussed the grut and got a clean print. It wasn't as good as it could be though. The area of the print where the extremely out of focus grut was projected showed a slight lack of contrast.
I won't get my lens as clean as I want to get it because that particle seems to be inside the lens on an inner surface. My best bet is to remove the lens and put a neutral density filter in the negative carrier so that my exposure times are not horrendously short.
I don't usually trigger the shutter release until I'm happy with my composition. I avoid contrails and power lines too.
On a serious note, I always de-focus the enlarger to the same place, raised the same height, same aperture and same negative carrier in place.... not sure if it adds to consistency of light or not, but it might. Fewer variables to think about!
I've tried all sorts of stuff. My current set up is--
An enlarger for a light source, any format. I currently use a bargain Meopta 4x4
A Mark Time timer left over from college.
A Kodak Exposure guide (I think Delta makes these now,) or just cover the neg with an opaque piece of cardstock and expose strips of the negative in 1 second intervals.
A short string of red LED Christmas lights bought on post holiday clearance.
I like my printfile contact proofer over a sheet of glass or contact frame. I find it easier to keep clean of finger prints, easier to load and unload and not much danger of dropping the glass and breaking it.
A set of 11x14 trays. Mine are old Kodak Dura-flex in spiffy Kodak yellow.
A VersaLab print washer(yeah I'm spoiled. You can get an attachment for a tray to make your own print washer if you want.) I used to know of a guy who claimed he washed his prints on the floor of his shower.
A sheet of glass and a squeegee.
A blotter book
A heavy flat weight---some coffee table size books work OK for flattening. A dry mount press works great too.