For most beginners, 4-string is the right starting point. The 4-string covers
nearly all rock, pop, blues, country, folk, reggae, and most jazz. The string
count is consistent with what most teaching material assumes, and the neck is the
right width for hand development.
A 5-string adds a low B string, which gives you access to lower notes used in
some contemporary music (heavier rock, metal, modern worship, some R&B, and a
lot of music written in lower keys for modern singers). The wider neck takes some
adjustment. Many bassists eventually own both, picking whichever suits the gig.
A 6-string adds a high C string and is a more specialized instrument, primarily
used in jazz, fusion, and progressive styles for melodic and chordal playing.
Most beginners don’t need to think about 6-string unless they’re
specifically drawn to those styles.
The honest answer is that 4-string is the default starting point and a perfectly
complete instrument for a long musical life. The other counts are tools for
specific situations.