Not a complete answer, but here's some more info.
Brightness
While there are ways to calculate this that aren't that complicated, it requires knowing many coefficients that are not readily available, so ends up being an educated guess at best. You can do just as well totaling your current lighting's lumen output, then adjusting for changes in fixture styles. (I consider even a simple LED strip a "fixture" for the sake of this discussion) It's a starting point. If you use proper task lighting, there's a lot of room for variance in total levels.
Uneven light
You do not want to see the actual LED elements, it's really annoying. Besides diffusers, indirect lighting techniques work well, though require more lumens due to losses through reflection.
Positioning
I'm not sure what the issue is with parallel surfaces. The efficiency is mostly inherent in the fixture's ability to direct light where it's needed. The mounting surface has little to do with this, you need to direct the light where it's needed.
White Light
The "whiteness" is measured in degrees Kelvin. The temperature a black body must be heated to emit the same color of light. Standard daylight is often taken to be 6500K, anywhere in the 5000-7000 range is close enough for most tasks. You eyes adapt quickly to small variances. In residential settings, daylight is considered too harsh because we are so accustomed to incandescent lighting, so most home lighting is produced to output more in the 2000-3000K range to mimic the orange incandescent lighting.
Noise
How audible the noise is varies by manufacture and environment, as well as personal temperament. I don't think noise data is readily available. Testing in a noisy store will not yield any useful data, other than if you can hear it from a few feet away it is too loud. Noise can be attenuated by placing it in an enclosure, but keep in mind power supplies generate heat that has to be removed by ventilation, you cannot seal it into a sound proof box.
Try to place power supplies as far from your pillow as possible, trying to sleep is when it will be most bothersome. Placing it lower so there is likely to be more furnishings obstructing a direct path will help, as well as being surrounded by soft materials that do not reflect sound as well.
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
1 Yes, it's possible to light a room with LED light strips. Lots of people do it. But it requires doing your homework. If you are impatient and fly past your skills, the project will probably fail. There are a variety of ways to do it.
2 You'll need a significant amount of 12V or 24V power (24V means half the current, which greatly improves the situation with voltage drop and fading). You will probably want dimmers and amplifiers. And appropriate wiring.
3 Given that this will be your primary light, you should place importance on CRI aka Color Rendering Index. If you remember green fluorescent and some CFLs and very early LEDs, that thing that made them look awful was bad CRI. Hold out for 80+ CRI preferably 90 CRI.
You should also be thinking about color temperature. 4000K is similar to fluorescents in an office. Old incandescents are 2700K. 5000K is similar to daylight and 6500K is a cloudy day. You don't want colors that are too blue in a bedroom in the evening, because they will make it hard to sleep. If you just buy random LED strips and don't pay attention, you will probably get 5100K, which will be pretty blue. LEDs naturally make blue light and use phosphors to convert it to other colors, so they like to sell you the more blue LEDs because they require less phosphor and are therefore cheaper.
RGB or RGBW lights let you dial in any color temperature you want, including some insane ones, but the CRI is fairly poor. I'm not sure I'd want to use RGB as primary lighting.
4 The product bundle you linked is a complicated bundle of products, including an LED strip, a smart WiFi based controller (RGBW dimmer), and a power supply. You probably don't want to use that. If you want control via WiFi or Alexa, then look for a-la-carte controllers or dimmers that do that.
Keep in mind that the electrical and building codes require that you have a light in the room that responds to a physical switch in the usual location. That can be a smart switch talking to a WiFi or Alexa type system, but it has to work when you push it.
All the wiring needs to be done consistent with NEC low-voltage rules. If your power is over 55 watts (which is actually a lot in LED), pay close attention to those rules.