I too started with the Stanley #5, which served as my scrub plane, my jointer and my shooting plane for the first year. I then found the Stanley #6 at a flea market which I used for jointing as well as shooting (because of the higher mass) and a block plane.
I now have a LN 62 which I love and reach for in most instances, but found that if I’m working with some squirrelly grain I would need something with a higher angle frog to avoid tearout. This is especially true unless you want to take very thin shavings and lots of passes with the low angle tools.
I would suggest a shoulder plane next. This will enable making tighter tenons. After that, you will have developed enough experience to know what to get next.