I think it would be a better idea for President to nominate Supreme Court justices for a fixed 15-year term, without the possibility of reappointment, thus preserving justices' independence from political pressure, but also preventing somebody staying on for too long.
Right now, with a lifetime tenure, a nominee's age is the primary consideration: must be young enough to serve as long as possible. And, on the reverse, Garland's advanced (for a Supreme Court nominee) age was a factor that was intended to make the GOP more willing to confirm. To be fair, RBG was already 60 when nominated, though it also should be noted that she wasn't first, not even second Clinton's choice. The process of finding White's replacement was pretty convoluted, with several candidates passing on (like Cuomo), or being passed over (like Breyer, due to the "nanny problem").
Fixed 15 year terms would definitely be an improvement over what we have right now. However, it could create some political pressure on justices to step down earlier to allow an outgoing prez of their party to choose a replacement in his final months in office. For example, if RBG's term was up in mid 2017, Dems may have pressured her to resign earlier to allow Obama to make another 15 year appointment. Or a prez doomed in his reelection bid could force justices of his party to leave a few years early to fill their seats rather than his likely successor. You could limit the number of appointments per year or presidency, but that may prevent filling vacancies that arise from death, impeachment or resignation for other reasons (health issues, corruption, etc.). There is just no perfect solution for less partisanship on the court.
A smaller question with fixed terms is how to deal with a hire to be Chief Justice. Does an Associate Justice who is hired to be CJ after 7 years on the court just serving for 8 more years, or is this considered a new term?
To be fair, I think most proposed amendments providing for fixed terms (be they 15 years or 18 years or whatever) mandate that appointments to fill unscheduled vacancies (which the bolded situations would technically be) are only for the unexpired portion of the term, & not for a new 15/18/whatever-year term in its own right (in which case, that seems like a pretty good - if not perfect - solution), though somebody can correct me if I'm wrong on that one.
