It goes without saying (but I'll say it anyway) that the "best" way of doing something depends on a lot of factors.
The "best" in terms of *easiest* is probably to just go mining or spelunking the old-fashioned way.
In terms of early-ish game automation, turtles and quarries can net you quite a bit of quartz, although that requires you to also wade though stacks and stacks of other stuff, and you may not end up with as much as you need, as quickly as you'd like.
Bees are a good bet, assuming you've got your bee breeding facilities up and running, have been to the end in order to start breeding, and have the multi-block bee thing to ramp up your income. Bees are usually mid-late game for me, so this isn't usually my first go-to, nor are quantum bees the first I breed.
The laser drill with the appropriate focus requires a bit of up-front investment - for me, the pink slime is always a pain. Assuming you can build it, though, the big thing is that you need a pretty stable power infrastructure to power up you laser to mine stuff at the speed you want. Capping it out with two prechargers requires 4 ultimate hybrid solars, or some equivalent amount of crazy power.
Depending on what you've got set up, any one of these could be your "best" option. Personally, I start with lots of manual and quarry mining, and try to get to laser drills ASAP, and bees are usually my last stop for whatever resource I need more of, particularly quartz.