Ooh, you're in for a treat! Bring on the conflicting answers...
Wet flies - I like everything to sink. I don't differentiate between leader and tippet - I usually just fish a level leader. Unless I want the flies to fish near the surface, then I might try keeping some of it afloat.
Dry flies - on stillwaters - with a bit of a ripple or a wave - I'll just want my tippet to sink. If the whole leader sinks then it's more likely to take the fly down.
Dry flies - on stillwaters - in a flat calm - I'll want all of my tippet and a goodly part of my leader to sink. Many's the time I've seen fish come up and look at a fly then turn away. Later, they'll take it confidently. And the only difference has been whether or not there's an obvious line on the surface of the water caused by the tippet or leader.
Rivers? I know better than to advance an opinion. I'm still learning...
Neil