Transistor Choice for LED Control Circuit
For what you're doing, you're gonna have to rethink a bit. From the data sheet, it appears that each 2" segment looks like







simulate this circuit &ndash; Schematic created using CircuitLab

Since each LED should have a current-limiting resistor, you'll need 450 of them, about 500 ohms, 1/4 watt each. The resistors will need to be mounted somewhere where they have good airflow, since they will dissipate about 100 watts total. (10 amps times 12 volts is 120 watts, and it's got to go somewhere.) Just bundling them together and putting them in a hidden box is almost certain to cause Bad Problems.

Your final assembly should look something like







simulate this circuit

except extended to 150 units. 

Each of the 3 drive lines needs to provide 12 volts at about 3 amps, or you can drive all 3 simultaneously with a total of 9 amps, so a 10-amp supply will probably do. There is a small chance, though, that driving all the LEDs on may draw slightly more than 10 amps, and the power supply will get unhappy. I don't have enough information to be sure. If you want to play it safe, cut back on the current a bit and use something like 560 or 620 ohm resistors. You may even want to mix values a bit to produce different drive currents, in order to get just the color you want. Experiment on a single segment before you commit to a final design. Be aware, though, that if you drive all of them the result will be (approximately) white. If you only want to produce amber light, don't turn on the blues. As a matter of fact, if you only want amber, forget about hooking up the blue leads entirely and cut your workload by 30%.

Your logic schematic is not ideal in this case, since your master drive could easily be folded into the 3 color drive signals, but I'll keep it anyways. 

The master drive is relatively easy, and can be done with an NPN transistor, or actually with an NPN Darlington (you won't get 10 amps with a single stage driven by LSTTL logic). What you really want is an n-type MOSFET. Your drive circuit would look like







simulate this circuit

The MOSFET should have a current rating of 20 volts or better, and 10 amps or better. However, that is very modest as MOSFETs go.

The 3 color channel drives are a little trickier, and for these you need p-type MOSFETs. The circuit is complicated by the fact that LSTTL will not handle 12 volts on the output without Letting The Magic Smoke Out, so you need to make slightly more complicated switches.







simulate this circuit

I've shown the NPN buffer transistor as a 2N3904, but almost any small-signal NPN will do. 2N3904s are cheap and readily available. Try someplace like Jameco.

I hope this helps.