I'd suggest that you take some time to review what you might build then prepare a parts list so that you can start shopping. Many of the tutorials are written by the same person and the circuits tend to use common components. The author's appear to be sensitive to parts procurement and tend to stick within a limited list of values for components. I've got some of the Radio Shack books that share this characteristic. The reward for doing all this is that you'll have what you need on hand to actually build something the way it's described.
Worth considering are the 50 in 1 or 200 in 1 experimenter/trainers that can be had at reasonable costs. On the surface they appear to be toys for kids but parts are parts - electronics is the same. There are also more advanced trainers if money is less of an object. If you want to duplicate something - purchase the parts then.
At some point you'll want to experiment a little - that might be the time to expand your parts inventory. What to buy is determined somewhat by the general area that you work in but you'll start figuring out what you need. At that point it might make sense to purchase the resistor assortments offered by Radio Shack, Jameco or similar distributors.
With all that said don't turn down someone's offer of free stuff. More than once I've had friends stop by who were just starting to learn about electronics. I'll grab some plastic bags and toss in a few items that I have as extras to get them started. Discarded electronics can be a good source too but be careful that you don't expose yourself to harmful substances.
It seems like collecting a bunch of parts - more being better than less - just seems like the place to start. I won't argue that it's a ton of fun but at some point the excess inventory can get in the way. There is something to be said for improvising - making do with what you have. That's something that's best done by the experienced.
Common transistors that I see used in simple circuits -
2N2222A
2N2907
2N3904
2N3906
MPF-102 (FET)
2N3055 (power)
Diodes/rectifiers
1N914
1N34A (germanium)
1N4001 series - look at Jameco
Common ICs
LM741 op amp
LM339 comparator
LM324 op amp
LM386 audio amp
LM317 variable voltage regulator
555 timer
I wanted to give you something. Realize that I live here in the US so these items are easy to come by.