There is almost no such thing as too much brightness on screen and almost all projectors can be setup for more or less brightness depending on your needs. This question gets asked several times a year and I've seen it dozens of times over the years.

Don't worry about it.

120" is a VERY typical screen size. Any common, decent projector, will handle 120" without any issue.

I would not use a grey screen in a good room with that projector. Positive gain grey screens have to use optical coatings which introduce sparkling and other negative screen factors. Don't use them if you don't have to.

In a proper, dark room, dark walls, dark ceiling, dark carpet home theater the professionals (Stewart Filmscreen, DaLite, Draper) continue to recommend a white screen or a slightly grey negative gain screen as the best option.

The Silver Ticket screens are a perfectly acceptable entry level screen.

If you look at the throw distance calculator for that model and set the screen size slider to 120" diagonal, you can see that the Throw Distance slider to the left of it has a blue range highlighted that says 12'2" and 25'0". That's your available throw distance for that projector. You can't put it any closer and get a 120" diagonal. If you have less than 12' lens to screen you would need to go with a 110" diagonal screen with that projector.