http://www.wikihow.com/Convert-a-Computer-ATX-Power-Supply-to-a-Lab-Power-Supply
As much problems your having find you a old PSU from a computer kind with a switch to turn on and use that
most have up to 30 amp output on 5 volt and about half of that on the 12 volt.

Do you really think you'll use that much power. The link the OP posted said bust up to 2 amps The Lm78 can handle 2.2 Amps in short burst.

These burst of the  SM5100B cellular module only last 4.6 mS

It's a OPTICAL INTERRUPTER something  like this one H21A1

Here a NPN setup

If you really need 3amp, you can look into the datasheet of your voltage regulator to see  how to expand their current capabilities.

I posted that for the OP he said in some kind of simulator it didn't work

I guess they put that in there data sheet for looks It works.

Get 2 tip42

You don't want to do that there not going to do what you think. One will try to put out more the it should and basically cutoff the second one. See there not going to supply the same voltage.

I would do this use a PNP to get you more current

Yes there is I'll post you something today.  You can sink 120 mA with a 5 volt supply

No you don't want 250mA. This chip gives 120 mA your led is good for 150mA Constant-Current

You can't drive them at 250mA Constant-Current that's pulsed 250mA the TLC is pumping of the current to give you a full 120 if you set it for that.

Now if you want more read this http://sonicrobots.com/wp-content/uploads/2012/07/arduino-tlc-5940.png

Yep these chips are nice but there a lot better chips for driving a bunch of leds. That one pin gray scale looks nice and is but it was made for Led arrays not led strings.

You no this changes the whole ball game these chips can only sink current.  But can be done there a appnote that shows how to do this.

To help you we need more info like how much you want to drive the leds, voltage,

Not all mosfet or bj are the same and voltage and load are needed to help you.

I would go for 20 volts then R1 would be 3k  and R2 1K  I would use a 2K Trimpot feed 20 volts to it and set the center dead on my VREF.

Test drive it with these values

Ct=436 pF
Ipk=440 mA
Rsc=0.682 Ohm
Lmin=50 uH
Co=98 uF
R=180 Ohm
R1=1k R2=3k (5V)

The voltage divider has to be set for the AREF to get a true  reading  You pick a voltage range 0 to 15

Then you pick the resistors to read full scale at your AREF voltage is how you get a true reading.

@be80be
Why the extra 1K resistor before the A0-pin?

I will save you from making a bo bo it limits the current