I do grind freshly roasted coffee when the beans are still a bit warm. Letting them set a day or so will let more of the aroma come to the surface of the beans and be noticed as the beans sweat oil, and sometimes that happens within a few hours, but the resulting flavor of coffee from those beans ground right away or a day or two later is mostly the same. Takes about a week before I start noticing a reduction in flavor. Grinding the beans when still a bit warm lets all the off-gassing occur that needs to occur without waiting.
Using the AP offers a lot of options, inverted or regular, water temp and so on. But I've noticed the major flavor differences asides from the bean selected and roast used come from grind, length of time of grounds steeping, and pressure applied. Though temp is important, I always start with water at 186F.
I can't get higher pressures with the steel screens, but using two paper filters works fine. Also a fine grind helps to get higher pressures. I do seek higher pressures for the most pronounced and desirable flavors.
My preference is limited time steeping (bloom, add a bit more water and stir, total of 30 seconds) and use higher pressure, which makes a less acidic and more malty cup. With lungo sizing (lungo is larger than a typical espresso) so water to 3/4 full when inverted about 2:1 water to grounds. The grind is using a manual burr grinder ($14 on Amazon) at the finest setting.
The result is drunk black and savored like nothing else that passes my lips each day.
A larger grind produces less acidity for me, unless the grounds steep a bit more, say 2-3 minutes. But the larger grind tends toward lower pressure. Lower pressure tends to produce more acidity (which some prefer) and a more common cup. But fine grind, less steep and high pressure works well for my taste buds.
African and Central American/Columbian blends are my favs, each roasted individually, about 1/2 cup of green beans at a time in a hot air popcorn popper. Will roast a Burundi to FullCityPlus and a Columbian to FullCity and blend the whole beans after roasting. Takes a few minutes per roast, and I use a glass oil lamp chimney and threw away the cheap plastic top of the air popper (purchased for $15 off Amazon).
So total investment is about $30 for AP, $15 for roaster (the hot air corn popper), burr grinder for $14 and green coffee beans (~$8/lb). The coffee runs out rather quickly, but the rest lasts for hundreds of cups of the best ever coffee. Oh, I got the oil lamp chimney at a thrift store for $2, and no more beans ejected when roasting.
For me progressed from a tea drinker to coffee from time to time, to hand crafted coffee in specialty shops, to fresh ground using a manual drip or French press, to home roasted AP/MD/FP. I moved away from French presses due to the excessive acidity and find grounds that make it through, in particular after finding the AP. The AP paper filter works nicely.