A week ago I was proud of my new PC build accomplishment. Now I'm convinced I didn't get something right.

But, I'm glad to have the support of this website. Thanks to all.
When I 1st booted this morning, temps were 30-32C idle. After 30 minutes they're 36-39C idle. I'm going to investigate this soon, but, if the fan isn't seated correctly I need to know what to do & what to do it with.
1st, this fan was tough to install (for me at least, a newbe). It overhangs the MB's #1 RAM slot & crowded #2 slot so badly I had to exchange my original RAM choice to a shorter, heatsink type. That being said, maybe a different fan is in order; one with a more positive mount that leaves no doubt if it's seated. This site has quit a list
Top 5 Intel & AMD Heatsinks on Frostytech. No doubt louder but cooler.
If I re-install this fan, I'll need to clean both the CPU & heatsink with rubbing alcohol & what; any type cloth or only microfiber? Paper towel is a no-no?
This time use a rice-size amount of Arctic Silver? Should this be wiped evenly or let the heatsink do that?
If the black pins in the mount all protruded the same length through the motherboard and you heard a click, then your heatsink is mounted correctly. I assume you mounted it outside the case and did a visible verification of the black pins.
I suspect the nuances between a rice size amount and the thin stripe per Arctic Silver instructions are within the margin of error. By that I mean that if it runs cooler or warmer after reapplication, you would be mistaken to draw any conclusions. Likewise on the question of wiping evenly or letting the heatsink do it.
FYI, I got idle temps in the low 30s with the stock cooler in a 72 F room, not in the 20s. My idle temps with the Big Shuriken are about the same. I have never idled in the 20s with any processor or heatsink in 70 plus rooms.
If you are going very far down the overclocking road, get a new heatsink that pays little attention to noise.
My offhand guess as to your current situation is that you have done nothing wrong--your temps are normal for your heatsink/ambient temp situation---and that any readjustment with this heatsink is pointless. I don't see any reason to be unhappy about the build. The only exception is if the heatsink is in fact NOT seated properly---which is a possibility. But your temps are NOT way out of line and don't vary much from mine.
Clean the heatsink with isopropyl and q tips or a clean white cotton cloth. A purist would tell you to use lintless coffee filters.
Most importantly, decide on your commitment to overclocking. If you get into it seriously, get a new heatsink and obsess over temps, voltages, etc. If you don't get into it seriously, I wouldn't change a thing--per the results of your already completed tests.