You should also consider how you want to use the system, and how much it differs from your current one. If you just want enough for a trial one shot, the roll mechanics, and the basic key subsystems ( like Perception, saves, and attack rolls in 5e ) can usually be picked up on a read thru, a couple of character builds, and a mock encounter. A week or less. If you just wish to be a player, this is usually enough.
If you're going to be the GM, that first trial one shot should be enough to tell you whether you want to use the system more. If you do, you'll want to do more study. Bone up on on those areas that you were weak in, and just keep plugging on. If its complex enough or different enough, you may wish to run a series of one shots exploring what you need to.
For instance, when I was testing out Wild Talents, I ran a series of one shots with increasing power levels. When exploring Anima, it was one short adventure per subsystem. One with just the basics/martials only. One with just the Ki Adepts, etc.
This leaves aside any other mismatches between the system, setting, and players. When I was trying out Fortune's Fool, my players were actually disruptive to the point nothing was acheived at all because they couldn't buy into the default setting. A real shame, actually.