You could go in either direction I would think. However there could be some trade offs. Someone with a new sound and new direction might add excitement but the band would be quite different and the older music might have less relevance and/or create a divide in your fans (e.g. Van Halen). I would rather have someone who compliments the existing style while moving the band in new directions.

It does matter if you are established because the old music is still good and fans still like it. You want to be able to do it justice. Unless you no longer like your old music (e.g. Beastie Boys).

I don't think you need to reinvent yourself for longevity. The two examples you site haven't changed all that much over the years. The key in my eyes is making music that is relevant at the time you are making it. Also, staying with it over the years. Jon Bon Jovi , regardless of what you may think of his music, still sounds good (or the same) after their comback. Can you say the same for Vince Neil?

I see longevity in music the same as most other things. Hard work, practice, dedication, and taking care of yourself. It sounds a bit cliche, but you can't just party for ever.