Welcome to this wonderful sport! I hope you find it as enjoyable and educational as we all do. As for buying an assortment of flies, it depends which way you plan on flyfishing (dryfly, nymphs, wetfly, streamer) and what type of waters are you going to fish (small streams, rivers, small lakes, large reservoirs).
I'd suggest you go to the local flyshop in the area you plan on fishing. Here you'll find out the latest info on where to fish and what to use. For Big Bear Lake I'd recommend you contact KeithBigBear on this site as he float tubes that lake an is a guide for it too. I've never fished Piru but I'm sure someone from The Fisherman's Spot
can help you out. In Mammoth there are two flyshops I'll go into to get info. Try either The Troutfitters
or The Trout Fly
Since you are new to the sport I'd like to recommend you take a beginner's fly-fishing class at any flyshop. Or go to your local Federation of Fly Fishers (FFF)
or Trout Unlimited (TU)
affiliated club to take their beginners class for free or relatively inexpensive. Any of these classes will increase the learning curve. Good-luck!
If nothing above seems appealing to you than I'd recommend the following flies for starters. The first three flies in the dry & nymph list are suppose to mimic the three basic bugs that live in the water: Caddisfly, Mayfly, Stonefly.
Dryflies-Caddisfly, Adams, Stimulators, and Royal Wulffs.
Nymphs-Hair's Ear, Pheasant Tail, & Zug Bugs