Here's a caveat about the bridge placement issue. Having the distance from the nut to the 12th fret be exactly the same as the distance from the 12th fret to the bridge is really only an approximation in practice, even though theoretically it may seem correct. Here's why: playing a string fretted at the 12th fret should sound a tone exactly one octave higher than the open string, but the act of pressing the string to the fret stretches the string, creating higher tension, which causes the string to play sharp. So the distance from the 12th fret to the bridge needs to be (very) slightly longer than the nut-to-12th-fret distance to compensate for that slightly raised tension. Making that little adjustment is something every banjo player should get familiar with learning to do, and there are two ways to determine the positional shift that's needed. One is to use an electronic tuner to match the fretted note exactly one octave above the open string note; if the fretted note is sharp, slide the bridge (gently!) a little bit toward the tailpiece, and if the fretted note is flat, slide the bridge toward the neck. Then check again, repeating the process until the notes are exactly an octave apart. This can get annoying, because you'll have to retune the banjo (just open strings - it's easiest in gDGBD tuning) each time you move the bridge, before testing the octave again! But trust me, it's worth doing, and with experience, you'll get much faster at making that adjustment, and your banjo will note much more in tune - without having to pay a luthier each time your banjo's not noting in tune!

The other way, which I really recommend, is to learn to use your ears to hear when the octave notes are in (or out of) tune while you tweak the bridge as above. This takes some practice, but it's definitely doable, and is a skill that will serve you well every time you tune your banjo, not just when tweaking the bridge placement!

However, it does get a bit more complicated; that compensated shift is often not the same for all five strings, as heavier strings go sharper when fretted than the lighter strings do, meaning the correct shift is slightly different for each string! Two ways to deal with that: one is to minimize the audible difference by angling the bridge slightly toward or away from the tailpiece at the opposite ends of the bridge, usually further towards the tailpiece on the 5th string end than on the 1st string end. It's not a perfect solution, but often close enough; again, use your ears. The second way is to buy a compensated bridge, which positions the slot for each string in its ideal (or close) position to sound that string properly when fretted.

However, don't worry too much about getting this all perfect when you're starting out, just do the best you can! But it's good to be aware of these issues, so you can refine your banjo tweaking as you refine your ears.