Here are a few points which are easy to find on quick examination:
Headstock at the neck… check for cracks which are most common around the head where it angles away from the neck itself. If a banjo has taken a spill there can be small cracks which cause major problems. Sometimes the eye has a hard time picking them up so, run your finger along this area & hold it at different angles for the light to expose cracks. Replacing a neck isn’t terribly costly but on a budget you want to avoid it.
Neck gap where it joins the banjo. The neck joint should be snug where it joins the assembly. Larger gaps or weird angles can reveal a possible bad repair or replaced neck which is misfitted.
Fingerboard & frets… looks for excessive wear, especially on the frets. Most well used banjos have easily seen wear on the upper frets. Look for flat spots or grooves which indicate a need for redressing by an expert or possible replacement. Again, this is not a huge expense but you may want to avoid it.
Tuners should run smoothly and hold their position well. Geared tuners allow you to see (most of the time) if the gears are in good condition or are missing teeth. Friction tuners can be a little finicky as you want tension but not so tight as to prevent movement. Another simple thing to pay note to is the actual condition of the tuner ‘buttons’, which are made of material in lower priced banjos which do not fare well over time. Heat & sunlight exposure can cause them to become brittle and break.
Resonator… look to see if there are obvious signs of swelling, cracks or delamination of material. I find scratches to be of minimal concern as they come about from normal use and a banjo is a tool… scratches tell a story and I like the history they bring. That said, some folks want a pristine instrument with no flaws. If it is surface, I don’t sweat it… if it is cracked or delaminated there could be real issues which can impact performance or be costly down the road.
Metal components like the tail piece, hoop & brackets should also be easy to inspect. Ensure no brackets are missing or cracked. Check to ensure no thread tape, glue or plumber’s ‘dope’ has been applied to the bracket threads to lock them temporarily in place. (This is likened to sawdust in a transmission of a car… old trick from shady characters.)
Head of the drum should be checked to ensure there are no tears or cracks.
For the most part, other things can be adjusted and you can work with them but the structural integrity of the instrument needs to be there for you to really get some enjoyment out of it. On another note… you may want to get a good banjo expert to setup your instrument. This is usually not expensive and allows the minor adjustments to be made with much less frustration… it also ensures the head tension is correctly tuned to provide optimum clarity & tone.
All that being said, sometimes you can find a good deal and then trade up at a later point to get a better grade of instrument. I’m excited to see what you find and would love to see pics when you have something to share.
Best of luck!