A calendar that I like is the Solar Hijri calendar. It is aligned with the equinox.
Of names of days of the week, that can depend on the language; for English, the Germanic names is mostly good how it is, but I would suggest to change "Saturday" to "Lyeday" (abbreviated as "L"), and to abbreviate "Thursday" as "Þ" instead of "T" (the name written in full is still "Thursday"), so that they are now seven difference letter of abbreviation instead of being the same letters.
Of names of months, that can also depend on the language, although the existing names for the existing calendar are no good (due to the last four months being the numbers that are not the properly numbers of the months in the modern calendar, although changing the start of the year to the equinox will fix that anyways). Names based on seasons might be better, I think.
Of year numbering, I would propose a new scientific kind of "anno mundi" numbering. The year measurement is the Earth around the Sun, so we can start with 0 for when that started occurring at approximately the correct rate.
