Use a mixed-quantities, colored set

I don't use a single set with 1 of each die, but a set that contains variable quantities of each die. For instance the set that I'm using is Dice of Rolling^[1], which contains 5 purple d4, 10 red d6, 5 black d8, 5 green d10, 2 white d12, 2 blue d20 and 2 yellow d100. As they say with this set you get all the quantities you need for gameplay with the 5^th edition. For this set of dice, all the dice with the same count of faces are colored in the same, distinctive color, which greatly helps finding the dice on the table, accelerating the game by a margin (usually time lost with "Hey, anyone has seen my d8?", "Oops I rolled a d8 instead of d10, they're all the same color"). With this kind of set, you'll get to the meat of the game in no time.

We gained so much time with this that my players offered me a second set as a DM gift to further gain more time (but only marginally, I must say). Everybody likes this, and they don't even come with their own sets anymore: one set ruled them all.

To answer the comments, yes we lost time before that we don't anymore. The sets are big enough to provide for a party of 5 players and a DM, bar for the d20. So a few players still use their own d20. For the rest they take their damage dice at the start of the game and there are barely any dice changing hands, except the d20. I always keep 2 d20 for myself, being the DM.

_{1: Not affiliated in any way, just a very happy customer.}