It makes sense - look for "low voltage LED Lighting" to see what's available, or slide on over to Electronics to build your own.
Dimmable LED bulbs are those with drivers built-in that are "dimmable" - if just running controlled current to LEDs, they are all "Dimmable" (lower current, lower light) so, no, you don't want an LED described as "Dimmable" (nor one described as 12V, probably - a "bare" LED with no other parts attached is best when you are going to feed it controlled current.) If you purchase a "12V dimmer" pre-made, follow the dimmer-maker's suggestions on types of LEDs to attach to it.
LEDs are current devices, so controlling the current will give highly consistent light output (controlling the voltage, less so)
What watt power transformer should I be using?
You can use a power supply like the one pictured, rated for the amount of LED's you will be driving. Read the specs on the lighting. They should tell you how many watts per a given length of the strip. So if it says, for example, that needs about 1 watt per meter, then a 15-foot section would require a 5 watt power supply. Take your total length of 76 feet, and divide by the strip's requirements. It wouldn't surprise me if you ended up somewhere in the ballpark of 20 to 30 watts.
Can I run 14 gauge wire directly from a circuit 15 amp breaker to the transformer?
No. You can't put the power supply inside the wall, and you can't bring the wire out of the wall without going through a junction box. The best way to do this is to put a cord on that power supply, and plug it into an existing outlet. There is no need whatsoever to add a new circuit or connect these directly to a circuit breaker.
Can I plug in all 5 circuits of LED strips on top of each other to the output of the transformer?
Yes, you can wire multiple strings in parallel at the power supply. If the sections are short, you can also wire them end-to-end. Double-check the specs for maximum length of a single run.
Is this the recommended way of doing what I'm trying to accomplish?
The recommended way is to plug into an existing outlet. If your lighting requirements added up to 1000 watts, you'd want a new circuit. At 20, 30 or 50 watts, it is ridiculously small in household circuit requirements.
I would also like to add a on/off switch, do they make a wall switch for 12v?
Any switch can be used for 12v. I would put the switch before the power supply. Put a cord on the power supply like this cord with switch.
Can low volt wires come right out of the wall, or do they need a junction box before being connected to the LED strip lights?
The low voltage wires don't need a junction box, but they do need a junction plate, like those used for phone jacks.
Best Answer
I would suggest good old J-B Weld for joining plexiglass and metal, and thistothat agrees.
Rough up the mating surfaces with 120 grit sandpaper and be sure to clamp where you can. If you don't want the J-B Weld to show, you'll have to put the plexiglass angle above the aluminum channel. However, it will definitely be harder to get a good bond, you'll have trouble clamping it from what I can see of your design. If you don't care because it's in a closet, you could cut some scrap wood to length and place it underneath as a brace while the J-B Weld cures.