I just went through similar with my new gun. I went cheap and got a cheapie bore sight off Amazon, it lasted about 2 minutes before the laser died, and the sight got stuck in the gun due to poor fitment (had to get the cleaning rod out to push it out). So if you get a bore sight get a good one.
So far I have only shot it at the indoor range I have a membership at, and it is only 25 yards, but took me about 30 rounds to get the iron sights set, and another 10 or so to get the red dot accurate.
This was the first time I sighted in a gun though. It was done with me just resting my arms on the bench, no bag or rest used. If/when I sight another gun, I plan on getting a better bore sight, seems it would be much easier and faster to use
The outdoor range I use has both sand bags and blocks for anyone to use, and I will probably use those when checking 50 and 100 yard.
As for cleaning, I have always been a minimalist.
Pistols are cleaned every 500-1000 rounds, except for my carry. I shoot 50-100 rounds every range trip, and it gets a quick field strip, wipe down and quick lube while still at the range, and a thorough cleaning every 300-500 rounds.
My rifles are about the same. My .22 is only cleaned when it starts having issues (usually ~1000 rounds), and I am still figuring out how often I will need to do my AR. I cleaned and lubed it when I bought it, cleaned it after the first time shooting it (420 rounds), and have shot another 500 or so rounds through it since then, and will probably do another 250 rounds before stripping it to see how it looks.