1. Use as heavy as tippet as you can get away with. I've heard divided by 3, divided by 4, etc. It's not perfect, depending on which end of the scale, amount of current, pickiness of fish, etc. But generally for me:
Streamers - 2x or 3x
Sizes 8-12 - 3x or 4x
Sizes 12-16 - 4x or 5x
Sizes 16-20 - 5x or 6x
Sizes 20-30 - 6x.
2. About the only fish I've come across that I actually think are line shy are steelhead. 99% of the time, they are drag shy, not line shy. Of course, going to finer tippet can help with drag. But so can lengthening the tippet, so I almost always lengthen the tippet before deciding to downsize the diameter. If you're tippets too long or fine, I prefer to upsize the diameter before shortening, but I admit sometimes I get lazy and just shorten instead.
3. Remember, for dry flies and sometimes nymphs, your goal IS NOT to straigten out the leader on the cast, you want slack. A tight leader is guaranteed to prevent a drag free drift. The classic thing you're looking for is S curves, but some people even try to pile up the leader. If you typically fish across currents, one of the keys is to keep your tippet upstream of your fly, which can be accomplished with a reach cast and careful mending.