Banjo Setup

A banjo has about 100 parts, give or take a few, all of which are conspiring against you to make your banjo sound terrible.  In order to tame this tendency you have to know a few principles that will help you setup your banjo without causing it to explode.  I've made a 40 minute video on this subject but it is, by necessity, incomplete because this is a wide and deep subject.  Because there are so many different banjos, so many different head sizes, so many ways to attach the neck to the rim and so many types of tone rings, I can't be specific about all of these banjos.
What I can do is give you some ideas about how to setup your banjo and where the limits of an amateur banjo mechanic are.  Most of this is common sense if you know how a banjo works but there is a scare factor when it comes to messing with your expensive banjo.
This video is aimed at the player who wants to maintain his or her instrument, not someone who wants to make major changes or anything past changing the head.

Banjos come with disposable parts: the strings, heads,  bridges (which eventually wear out) and some parts such as the tailpiece (some of which have a tendency to break) or tuners which can be changed out.
Since a banjo is an accumulation of parts, an heroic player may want to try and change other things but for the most part the idea is to keep the banjo at an optimal state, i.e. each part snugged up to the right tension and safely in their places.  A banjo is the sum of its parts, but some parts are more equal than others.
Rim
The rim is the most important part of a banjo.  A banjo with a great rim will sound good even without a tone ring - look at John Carty's Ome which only has a simple metal hoop (of course he has something to do with it too.)  The rim is not a part that you can deal with, but the relationship of the rim to the tone ring and the head is very important.  The rim to tone ring fit is a matter for a banjo luthier (one like Vin Mondello or Charlie Cushman, not your local guitar guy) but the relationship with the head is also very important and you have some control over that.
Head
Changing heads can make an impressive difference in the sound of a banjo.  Fitting a head to a banjo can be tricky - you have to have the right diameter but if you already have a head that fits, just measure it.  You also have to have the right height of head and you should look up your banjo on the net to find out if you need a high, low or medium head.  Changing the head is a pain and if you don't like the results it is even more of a pain.  But if you have done all the work needed and don't like the results, don't give up yet.  After a head has been changed you have to wait at least several weeks as the rest of the banjo settles in and you get the head tension right.
Head Tension
The head tension is probably the one adjustment you can make that will make your banjo sound good.  There have been a lot of things written about this, but the easiest way to determine if your head tension is good is to listen to the banjo as you tighten the head.  It is a mistake to make large changes in head tension.  Once the head is snugly on, you can make big sound changes with very small tweaks of the tension ring as long as it is even all round.  The idea is to increase the tension until you like the sound and then measure what that tension is.  A lot of players do it the other way - they tighten up to a specific tension and declare it  right which is backwards to common sense.
The video shows a way that I use to tension the head and how to use a DrumDial to measure the result so you can go back to it again.
If you learn one thing, it should be how to tension your banjo head.
Strings
There are two things you have to know about strings in Irish tenor banjo.  The first is that the string gauge varies with the scale of the banjo.  There has been an unfortunate tendency of banjo marketers to call a short scale (19"-21" or so) "Irish Tenor Banjos" and sell them as easier to play.  While the short scale means less of a stretch to the high B note, it also means that the changes you do both in setting the bridge and the gauges needed to make the G string sound good are critical.  By critical I mean that it is a lot harder to find the right strings  that work with a short scale banjo and even a slightly long or short difference in length makes the banjo sounds terrible and causes the intonation to be bad.
String gauge can make a difference in sound quality.  Some banjos are sensitive to what the gauges are,  while others are indifferent.  The higher the gauge, the more the tension, so in older banjos a lighter set may be a compromise but it will preserve your banjo.  You can make up some of the difference with other setup changes.
The second is the material that the strings are made from.   I have several banjos that don't do well with bronze strings and others that love them.  You have to find out what material and what gauge works best for your banjo.
Here is an excellent way to change strings.
Bridges
There are four important issues with bridges.  The first is the bridge height which helps determine the action of the banjo.  Banjos are built for a specific bridge height in mind but there is usually enough room for some variation. Another little tip is that a bridge has a 90 degree side and a slanted side.  The slanted side, which usually has the logo on it, faces the headstock.
Second is the materials that make up the bridge.  The classic bridge is made from maple and ebony, but the quality of materials and how they are put together is very important and some banjos do better with other materials or no cap on the bridge. This is a complex issue that may only be resolved by finding a decent optimal bridge and then forgetting about it  because if you obsess too much about it you will never be satisfied and at $20 a pop that can be costly.
Third is bridge placement.  Because of the physics involved in how strings vibrate, correct bridge placement is crucial and often forgotten even by luthiers.  The videos show how it is done and it is simple enough that anyone can do it.
The final issue is that once you change a bridge, you may have to change the tension on the head or other aspects of the setup because a bridge change is a disruptive act for a banjo.  No part of setup is independent from any other part and any changes effect the rest of the banjo. Bridges are the only conduit between the vibrating strings and the rest of the banjo.  They act as a filter and the sound changes due to the material of the filter.  This can make a huge difference in how a banjo sounds.  Find a good maker and work with him or her if you need to change out the bridge.
Tailpiece
The tailpiece is usually not dealt with very much except in changing heads where you have to take it off and put it back on.  The main thing is that a tailpiece can change the sound of the instrument and it has to keep the string tension on the bridge.  If you have a low tension tailpiece like a no-knot you will probably not have the full power of your banjo at hand.
If you have to go beyond these setup parameters, you should either have some experience or find a good banjo luthier.   It is fun to work with your banjo but if you are afraid of it, you will screw it up so don't try.  Otherwise you can do the things you need to in order to maintain the sound you love.
Picks
While picks are not strictly a setup issue, they are the subject of endless speculation.  I find that you will eventually find the picks you love but will constantly be on the lookout.  No master player seems to agree with any other on what is an optimal pick with the possible exception of the Dunlop nylon .63.

Resources
Check the links below and above for other ideas about setup.
Banjo Maintenance from Deering
Richie Dotson tips
Speed changing the head 
How to tighten a bottlecap banjo using the alternative bolt pattern
Warren Yates on truss rods - Warren has a lot of good tips on his channel