Transistor part numbers are totally arbitrary and seldom have anything to do with a particular parameter. The best way to find one you need is 1) look through what you have, and if that fails 2) use parametric searches on distributors (e.g. Digi-Key BJTs or MOSFETs)
A 2N2222 (very common NPN) should be able to power 10x LEDs well.
You're using a moderate amount of current, so I might use an N-channel MOSFET instead of a BJT, it's the easiest to control and doesn't have a fixed voltage drop. A ZVN4206A would be a TO-92 that might work. Regardless between that and a BJT, you need a transistor with:
- A voltage rating, Vds (or Vce for a BJT), greater than your supply (1.5x or more recommended)
- A current rating, Id (or Ic), greater than the current that your LEDs will take (this depends on temperature; if you will be running it outside of room temperature you will have to derate this)
- A threshold voltage, Vgs(th), that will allow it to be fully turned on with your input voltage ("logic-level" is something to look for)
- For a BJT you need to make sure you can drive enough current into the base to saturate the transistor against the base-emitter saturation voltage, Vbe(sat).
Connect it like so (image from Electronics Tutorials)
(For a BJT, it would be similar, but Collector instead of D(rain), Base for G(ate), and Emitter--S(ource))
The "lamp" would be your string of LEDs, however you want to configure them. The diode isn't required for non-inductive loads (generally "things that aren't motors").
One of the advantages of this low-side switch configuration is your logic can be at a fairly low voltage (3.3-5 V), while your load supply voltage can be whatever your transistor can withstand (500-1000 V, whatever).
You mention this is for a specific LED flashlight project. If your main focus is powering LEDs, you could look at something more advanced: an LED driver. The Linear Technology LT1618 can step up voltage from 1.8 V allowing you to supply it with 2 or 3 alkaline cells, and provides current regulation, so you can eliminate all (or at least most of) the LED ballast resistors.
Example from the datasheet:
The LT1618 or a similar step-up regulator would provide you with the most efficient driving method, both from an electrical point of view and mechanical, as you can use more space-efficient cells (D > C > AA >> AAA >>> 9V)