Camps I sight in all my rifles in the basement or garage initially.
At this point I will already know what speed I'm shooting and my scope over bore height so I then use the desktop version of Chairgun to get a rough idea of where my Optimal Zero is and the nearest point where my pellet will first cross 1/4" below that zero.
With one of my tune and scope combinations my Optimal Zero is around 30 yards. At about 12 yards I'm a 1/4" below that zero and I'm a 1/4" low again at about 34 yards.
So for that tune I roll my pellet trap to 12 yards in my basement and site in my scope so I'm hitting slightly low at 12 yards. I don't get out calipers and measure 1/4", I just eyeball it for the initial site in.
This is with a Classic Leshiy in 22 around 700 FPS with a heavier pellet and a likely lower scope over bore height so I would anticipate your Optimal Zero would be a bit further out.
To answer your question of what is minimal yards to site in, I'm not sure. With the tune above I'd be an inch low at 5 yards and I guess I could zero in an inch low but I've never had to do that. If I did I would probably put a row of these self adhesive target dots at one height across my trap and then put another row centered an inch directly below those. And I do have a couple of scopes that come close to focusing at 5 yards.
What is the longest safe distance you have available in your basement?