The X system is for diameter.
1X = 0.23mm
For fly fishing diameter is more important then breaking strain and it is just easier to say 3X then 0.203mm or 0.008″.
There is three kinds of tippit material Nylon, Co Polymer and Flourocarbon. There is not much of a difference between the different types.
A comprehensive answer is there. (Although Fluorocarbons has poor knot strength)
http://www.kennebecriveroutfitters.com/ … ippets.htm
Generally, a co-polymer/nylon would be better dry fly fishing and Flourocarbon would be better for nypthing. But the difference is subtle. For starter purchase a decent quality Co-polymer. Co-polymer cost around $7 a spool while flouro is around $21. Rio is a good brand and is easily found. I beleive Umpqua and Cortland sell the same product as Rio but with a different brand. Airflo has slightly lower breaking strain then the others.
Go into Mikefishing or the fishermanloft and I certain you would get good advice. All of the chch fishing stores are good.
Maxima Ultragreen Line is also popular, that is just a typical fishing line. I prefer the more specialised lines.
At this time of year for general Nymphing I would probably start fishing with a 4X and if the fish refuse to take after several good presentations and fly changes I would reduce my diameter to 5X maybe even 6X. I would do exactly the same for dry fly fishing.
If the water is a bit cloudy you could get away with 3X, I use 3X early season when the fish are less wary.
Streamer or lure fishing requires a slightly different set-up. I typically use 2X or 3X. If the water is dirty I might use 0X or even 20lb line.