Second post, for fear of losing it all in one go.
The
Cree XRE isn't bad. The newer XP-G is more expensive but brighter at a given drive level (or more efficient for given output).
Scroll down to the list of radio buttons. The LED descriptions are as follows. I refer to charts in
this PDF
[Flux bin] Flux [color space] Tint ([low]K to [high]K) (+cost in cents)
P4 Flux 7A Tint(3200k to 3500K) (+0.49)
This is a P4 flux bin LED. On that pdf, the first page identifies the flux bins - the output at 350 mA drive current (1 watt power). This LED will emit about 80.6 lumens. The flux bin is -entirely separate- from the kelvin temperature, although warmer LEDs tend to be dimmer - there's more phosphor globbed on. You'll want a nice Neutral White in a high flux bin, because these will allow you to get the light you want at lower power levels. Q4 isn't on the chart, but expect about 100 lumens at 350 mA.
Briefly, the datasheet:
Page 4 of the Cree datasheet has some facts about the Cree LED, including the maximum temperature the LED can withstand - an infrared thermometer can approximate this when you point it directly at the diode. Page 5 gives the spectral distribution, showing the Green Hole and the Red Tail, both of which contribute to the corpseriffic look given to people under (cheap, cool white) LED lights. Page 6 shows the "Luminous flux at given junction temperature." You lose a percentage of light with an overheating LED. Page 7 shows the "Drive current at a given voltage." This is how LEDs are usually killed; a high-capacity source at a slightly-too-high voltage will pour amps and amps through. Page 8 shows the increase in output for a given current; LEDs are more efficient at lower drive levels. Page 11 shows the LED itself. The page numbers may be different for other Cree LEDs. Luxeon releases similar information for its LEDs, I haven't worked with them as much.
Planning:
Let's say that this statue will be in a fairly bright area (but not outside), and that you want about 180 lumens of light coming from below the statue. With a bare LED there are no losses for optics or diffusers, so we just want 180 lumens split among 3 LEDs (60 per emitter). That requires about (according to page 8) 200 mA per LED. Using page 7, we see that the forward voltage is about 3.1v. The heat from each LED will be approximately Current times Volts = .2 Amps times 3.1 volts = .62 watts. How hot will each LED get? Not too hot, but we'll want to account for some loss of LED output. Page 6 tells us that a 100 centigrade LED die will lose about 20% output - that's the boiling point of water, hopefully nothing we'll lose. In testing you may find that setting the LEDs at exactly 200 mA isn't enough, and you'll adjust it.
LED Wiring:
LEDs can be wired in parallel or series. With 3, you have to pick all parallel or all series. You'll need (at least) 3 times the LED voltage in battery, or have triple the current, or have a boost driver (electronics that step battery voltage up by sucking extra current; ex. turn 1 amp at 1.5 volts into .4 amps at 3.7 volts). If you do it with resistors and fewer batteries, you'll want voltage. AAs will hurt here; a 9v battery or CR123 may be a better option. You could really use any voltage source that can deliver the current and voltage you want - either:
200 mA and 3*3.1v = (at least) 9.3v
or
600 mA and (at least) 3.1v
The resistor to limit current will depend on exactly one trick. The voltage across the resistor is (Vbattery - Vled). The forward voltage of the LED matters here. Let's say you use 3 AA batteries in series (the ever-popular 2000 mAh Eneloop). On a fresh charge that gives 1.45 volts, and when it's nearly dead it will have dropped to about 1 volt. This voltage, 4.35v, is only enough to drive the LEDs in parallel.
Vresistor = I * R
Vresistor = (Vbattery - Vled) = (3*1.45 - 3.1v) = 1.25v
I = 3 * 200 mA = .6A
R = ?
1.25v = .6 A * R
1.25v / .6A = R
2.0833 = R
So a 2 ohm resistor that can handle a power of (.6A times 1.25v) .75 watts will limit the current. As the batteries die though, the LED will be dimmer. A slightly lower resistance will make the LEDs start slightly brighter, end slightly brighter, and kill the batteries slightly faster. A resistor of exactly 2 ohms will give you about 4% more power than we planned for, which is ok. The eneloops in series have 2000 mAh at 4.35 volts, and a 2 ohm resistor with these LEDs would drain them at about 625 mA per hour. These batteries alone would last for about 3.2 hours - 2000 mAh divided by 625 mA gives hours. If you'd used a high-voltage battery (9.3 volts or more) then you could run it at .2 amps instead, but the formula is identical.
Any questions so far? Tl;dr?