As Frank suggested, check out the FAQ in the link he provided. Just to give you an idea of what you’re looking for in shops here some links with pics.
For trout a 9 foot long knotless monofilament leader tapered to 4X like this one from Rio:
To the leader you’d add about 2 feet of tippet. For trout, I’d suggest a spool of 4X, 5X and 6X. Here is an example of a tippet spool from Rio:
For Bass, I’d get an 8 foot knotless mono leader like this one from Rio in 12lb test:
To the bass leader you’d add 2 feet or so of tippet (1X, 2X or 3X) or regular fishing line in 12, 10, or 8lb test which would be roughly equivalent to 12lb=1X, 10lb=2X, and 8lb=3X
If you can’t find Rio, there are other leaders and tippets out there from Umpqua, Climax, Scientific Anglers etc.
As for a fly line, you’d want a weight forward taper, floating line in the weight your rod is designed for—so a 5 weight line if you have a 5 weight rod. It depends on your budget, but I’d go with a 40 dollarish line from Scientific Anglers (SA) or Rio if you can swing it, but here are some options at different price points:
Around 25 bucks: SA Air Cel
Just under 30: Rio Mainstream, or Cortland 333+
Just under 40: SA Aircel Supreme 2, SA Professional Series, Rio Classic, or if you have a fast action rod, an SA Head Start (a slightly heavier than standard line)
and it goes up from there.
Another thought is to look for a deal on an SA Ultra 4, which is being phased out and replaced by the SA “Supra” for 2009. The Supra line sells for just under 50, so if you can find an Ultra for around 30 or so, that would be a good deal. It’s a pretty nice line.
As for backing, Cortland 20lb Micron would be good. Get a 50 yd spool if you have a small reel with 50-60 yds or less, or a 100 yd spool if your reel holds more than 75. (a 100 yds would be plenty, so even if your reel holds 120yds of backing with fly line, 100 yds will be fine). If you can’t find Cortland, then Scientific Anglers is good too.