Sharpness is all about controlling technical variables. A subject with details and contrast in the center and corners is good. Lighting should be consistent for maybe 30 minutes to an hour. My house is brick so I've used that, and we get a lot of days with no clouds at all. Bricks are supposed to reveal distortion but it's hard to see. At 300mm I used a house about 4 houses away. I try to get something about the same distance as where you'd use the lens. If you are at the minimum focus distance, field curvature is more significant and can make lenses with a lot of curvature look bad in the corners.
Recently I tested some 24mm lenses in a garage, taping some newspapers up like this:
The lighting is clearly not even, but that's not a big problem. It's consistent. It was very handy to use the post-it note to identify the lens. The results were useful. My wife ran over my tripod, though.
For sharpness, focus is all-important. I mount a lens, focus as well as I can, run through several apertures, then do the next lens. I repeat the whole test three times. If I'm careful, I can get focus right for most lenses for two out of three tests. But I always have one or more series that is clearly worse.
I try to establish one exposure for a "middle" aperture with one of the lenses, then shoot them all based on calculations from that. For example, I pick a lens and put it at f8, then find a shutter speed that gives an "exposed to the right" histogram. If the shutter speed is 1/250, then I shoot every lens at f8@1/250, f5.6@1/500, f4@1/1000, etc. That avoids metering and differences in mounts.
What I like to test is sharpness like this, flare with a strong light source on the edge of the frame, and colors and contrast by going to a botanical garden. With a group of lenses, that's a lot of shooting.