There is a discussion in the Poskim whether one should purchase Arba Minnim during the Aseres Yemei Teshuva in order to increase your Mitzvos prior to Yom Kippur or should you wait till after Yom Kippur when you are more pure and thereby you will get a nicer Esrog that mirrors your purity. Any other thoughts on this subject would be appreciated.
There's the general question of doing a mitzva sooner vs doing a mitzva better. Of course, if there's ever a doubt if you'll get the mitzva later, definitely seize it now!
Some point to the Radbaz who seems to say do it sooner.
Our practice is usually to wait for kiddush levana till motzei shabbos (and/or post Yom Kippur or Tisha B'Av; post Yom Kippur is especially interesting as that's one more mitzva we're not yet racking up before Yom Kippur), implying sometimes better can beat sooner.
The question was even raised, "should I get married now, or wait until I've done some more personal growth? Get married sooner, or better?" I believe the recommendation is often better as long as it's not too much later.
So the question is out there, and each case probably gets decided on its own merits.
I have heard (IIRC) that the Brisker Rav zt"l would specifically do it during Aseres Yemei Teshuvah, because he felt that this was part of the avodah of these days. Rav Aharon Kotler zt"l, however, would wait until after Yom Kippur, because he felt that the avodah prior to Yom Kippur should be focusing solely on teshuvah. (Or something like that.)