So is it best to let the game fully install first before actually launching it? More or less how are the install times?
The launch games and the games that shipped in the first few months had awful install times, partially thanks to the 180 on the always-on implementation, so their install code wasn't as polished as it should be because they had to retool to allow for working in an offline environment, etc. IIRC Ryse took something like 15m before it was "playable" (which in their case meant... you could stare at a menu screen that wouldn't let you progress any further), and something like 45m to be fully installed.
Things have definitely improved since those early days, though.
The most recent disc-based games I've bought were Wolfenstein and Watch Dogs back in May, which were both playable within a couple of minutes, and Destiny, which had a really stupid implementation where you could launch it after a minute, but then it just showed you an install screen telling you how far along the install was. Everything else I've bought recently has been digital, so I can't really comment on install times.
One thing to bear in mind if you're coming from the PS4 is that the way it displays install progress is different - the PS4 shows a progress bar that only covers the initial install necessary before you can play, then the rest is handled silently in the background, while the XB1 has a progress bar that covers the
entire install process, with it giving you a notification when it hits the point when it's playable, which varies by game. So even if a game took exactly the same time to hit the playable point, I think that implementation makes it
feel slower than the PS4.