I would like to build something similar with the following features
Use an electret mic for the sound pick up that I can adjust the sensitivity of
Be able to set a delay in micro second from the sound to camera/flash release
I have a SainSmart LCD Keypad shield, so use the keys to set the delay and have it displayed on the LCD
Arm the circuit ready for the sound
Trigger the camera/flash I think 1 output would do
Indicate on the screen after release
Then re arm itself after a set time
Use a arduino uno with a atmega328p
As I mentioned before all of these are within the capability of the Arduino, since both TriggerTrap and CameraAxe already support it. I happened to have bought the original TriggerTrap
So your hurdle is to learn how to program your Arduino. Now from my perspective as a professional programmer for 34 years, the programming is rather straight forward. But you are going to have to take it one step at a time. Rather than trying to build the whole project as one complete finished project, you need to break it down to smaller steps.
The first step is just to get comfortable with the stripped down version of C++ that they use for the IDE. Take the blink example, and modify it to add different delays, learning how to download and modify the program.
The next step is probably to add your sound trigger, and set it up to turn on the led when it hears the sound. Initially you will just need to program in the details directly to the program, iterating, changing values until you get an initial value to work with. You probably want to turn on the led when you hear the trigger, and then turn it off after a given delay (such as 1 second/1000 milliseconds).
I would imagine the next step is to learn how to write to the LCD shield, and how to read buttons.
Then you want to combine the LCD shield with the sound trigger, where you have a menu asking for the various things to change (delay after sound before the led is fired, sound level to fire the led, delay before arming the sound trigger, etc.). This will need to get you to think conceptually about saving state, and using it in the program.
Then you replace the led with an optocoupler to fire the flash, and you have your first prototype. If you are are firing a camera as I mentioned, there are several different ways to fire a camera, and what you use depends on your camera. After your first prototype, then it is a matter of iterating, adding features, fixing bugs, etc.
At this point, you may want to start looking at the blink without delay example, that many find challenging, in that you have to adjust your way of thinking from doing everything as a straight line program, to having a state machine in the program that lists the things you want to do, and when you want to do them. Or learn how to do things via interrupts. For your current needs, you probably can get away with not doing this, but eventually you may need to redo your code so that the Arduino is doing multiple things at a time, such as waiting for menu presses, and doing the sound trigger, etc. As I mentioned, this can often times be a big conceptual block to many people. At the moment, while I have created state machines for other projects, I haven't done so in an Arduino context.
Sure, it will take some amount of time to come up to speed on this, but if you don't come up to speed on the programming side, you will only be able to use things that others create. It can be rewarding, when you come through the process, and are able to create things from scratch.
At the end of the day, if you just want a prepackaged solution, those are available. However, they don't come cheap. So you need to figure out whether it is worth it to learn how to do it yourself, where it will be cheaper, but take longer, or go for the prepackaged solution.
I mentioned triggertrap (TT). I bought a triggertrap when it was in its initial kickstarter phase. At that time, the triggertrap people seriously underestimated all of the problems in bringing something from a hacker design to making a real product, and the project was delayed by almost a year from the original projected date. At the same time, they realized that they had seriously underestimated the cost to build products as a full time job where you need to pay people to assemble it, procure parts, etc. The upshot is while I bought the triggertrap V1 for $75, the cost of a prefabricated TT is now $200. Now, personally, I haven't used my TT all that much, because I got frustrated by the delay, and discovered the Arduino while I was waiting for the delivery, and also my photographic interests have also changed. However, I might use the TT for an upcoming project, since I already have it, and can now reprogram it. As an experiment, I just got the TT out of the box, plugged it in, and in a few minutes I was able to get their sound trigger to work when I clapped my hands, programming in a delay.
Camera Axe is a competitor to Trigger Trap. I think it predates TT, but I wasn't aware of Camera Axe until after I had bought the TT. From glancing at their site, the Camera Axe people are more setup for hackers to work/extend their product. Their finished retail version is $185, but you would need to add the microphone (TT comes with a microphone built in). Unlike TT, they have more sensors available at their store, and have a hot-shoe for firing flashes.
Midway between making your own system, and buying a retail version, is using either a trigger trap or camera axe shield that plugs on an Arduino. You would have to be comfortable enough to solder all of the components together (I wasn't at the time, and still don't like soldering). The trigger trap shield is $50 and it includes the lcd, laser/sound triggers, etc. The camera axe shield is $85, and it includes the lcd, but I'm not sure it includes sound/laser triggers.
Finally, Trigger Trap has moved to supporting both Apple and Android phones with a free app, but you need to buy a $30 dongle + a camera specific cable. Unlike the Arduino based versions, I don't believe the source is open for the phone apps. I have the Android dongle and app on my phone, but unfortunately the Android device does not support the sound trigger. The Apple app does appear to support a sound trigger, but since I do not have any Apple devices, I don't have any experience with it.
I think this is the original video from the camera axe guy explaining the basics: