Playing: Can you recommend one particularly good beginner instruction video? or book?
Homespun Tapes. Happy Traum's. Get Pete Seeger's book, "How To Play The Five String Banjo". Get David Holt's tape from Happy. Get Happy's instruction tape for beginners. Check with Janet Davis Music
What are some good skill building drills?
Learn the basic strum first. Some use the index finger, some use the middle finger. Down on one string as if you were hammering a nail with your index or middle finger. Then brush across the strings either the same finger. Or you could use the first finger down and brush down with the others. Then, play the fifth string with your thumb. An instruction tape as suggested above will clarify this. The "Bump ditty" strum is counted in music notation as "one, two-and" the first being a quarter note and the second two as eigth notes.
What skills should I work on early to make learning new tunes easier later on?
Learning the basic strum. Eventually, drop-thumbing or double-thumbing but not at first.
How should I structure my practice time?
Have fun. If you want to get good, have the banjo in your hands at every opportunity as long as you don't get tired. The best practice is distributed practice, not mass practise. Do little bits at a time throughout the day rather than a lot of hours at once where what you learn gets broken down and less affective.
How should I approach learning something basic for playing along at a song circle?
Learn to sing a song and accompany yourself with the basic strum.
Buying: If I can only play one tune, how should I 'try out' an instrument?
Listen to the recordings of those players you like and find out what they use. They are different.
What do I look for?
You might consider the Goodtime Banjo by Deering because it's pretty good sound and inexpensive.
What's with the tone ring? What is the difference between the types of tone rings?
It's the tone quality of the banjo. They differ. The Mastertone tone ring is a lot different in quality than the tu-ba-phone for example. There are fretless banjos, gourd banjos, minstrel banjos and electric banjos. They use different tone rings and sound different.
What difference does the bridge height make?
The higher bridge is generally preferable for frailing or clawhammer. But the action has to be adjusted so that the strings are not too high.
What about the material it's made of?
Different materials. One maker I know uses a Brazilian seed...tocoa wood which is hard like ivory. There are plenty of good bridge makers. A good reference is Dick Weissman's book on Folk Music.
What about the string gauge?
It depends on the banjo type.
What's the difference between 11 & 12 inch pots?
11 inch pots are more standard. The larger the pot, generally, the lower the frequencies. More boomy.
Apart from weight, what's with the different number of brackets?
The more brackets is generally a sign of a better banjo.
If I start out with a light instrument, will a heavier one later be a big adjustment?
Every new instrument requires an adjustment. You have to live with one banjo for a while to get the hang of it.
A note on styles. The current popular clawhammer style is the "round peak" style as practiced in the Mount Airy festivals in VA. Tommy Jarrel, Kyle Creed et. al. For this, you might need a lighter instrument, not a long neck. Stewart, Cole, there are many of them. Early Bacons, also. You can even clawhammer on a Mastertone and it sounds good but the style is usually an open-backed lighter instrument such as a Vega Whyte Ladye.
Any other important construction considerations?
Decide which clawhammer style you like. Uncle Dave? Round Peak? Clarence Ashley? Buel Kazee? Then find out the banjo they play and go for it.
What would you recommend for <$1000?
Do some homework on the available lines. Deering, Ome, Wildwood(?) Bart Reiter? Go to banjos on internet and look there. Don't be in a hurry to buy anything. do the research.