I know this started out as an older thread but I have a couple suggestions.
1. It is so important to remember that water profile is important for two reasons: mash pH AND flavor profile. And these two goals are not always met in the same way. AG brewers will need to consider both parameters while extract brewers only care about flavor profile.
2. IMO RO/Distilled is a much better starting point than tap, even if you get your tap analyzed. The reason for this is that in most places the source of your tap water can change - and it is almost guaranteed to change at different times of the year. And as far I know the water supplier doesn't send a card in the mail when they do make a switch. If you start with RO/Distilled you are taking this potential variation out the equation - and it is not hard to find water reports showing the variation to be quite significant.
3. I personally recommend creating your own target profile based on the intended flavor you are trying to create. This brings the science to a more personal level - and intentionally so. The goal here is to make good beer, not tasty water.
There are so many resources for this, but when I start a beer I go to section 15.1 of How to Brew
http://www.howtobrew.com/section3/chapter15-1.html and put together my target profile based on the intended flavor and color of the beer I am going to make. Keep in mind we are working in ranges here - not exact numbers.
Then using an online/spreadsheet calculator I put in my water profile (which is all zero's for RO/Distilled) and then enter the target profile I created. Using a water chemistry calculator (I use brewers friend
http://www.brewersfriend.com/water-chemistry/) I come up with the additions I need to hit my flavor profile - and if I am doing AG then I am also looking to hit the correct mash pH.
Done.
Most water chemistry calculators will have some sort of safety feature to alert you if you start going crazy with your additions (at least I know the one I use does). This is an important feature to look for.
4. IMO you really don't need an extremely accurate scale. We are using very imprecise ballpark numbers to begin with, so it seems non-value added to spend any amount of effort on being precise. As long as you have something that can measure down to the gram that is good enough.
5. Additions should be added at the respective stages of the brew.
For extract brewing everything goes in the boil kettle.
For AG, assuming you calculate your additions for the total boil volume you would add a pro-rated amount according to the strike water volume in the mash tun, and then the rest can be added in the boil kettle. If you try to add your additions to the strike water or sparge water in the HLT that won't work. The salts will precipitate out, so you want to add only to the mash tun and/or the boil kettle.
6. As I mentioned before - I am pretty sure that most of this information is not scientifically verified. That doesn't make it wrong or bad but the best thing you can do is try some experimentation to find what works for you. I think this is almost a necessary step.
7. In light of all of this I encourage you to think about the water profile as a part of the recipe. I know in my experimentation that I can make a the same recipe taste incorrectly bitter or overwhelmingly sweet - all by altering the water profile. This influence on flavor should be considered as another variable in the recipe - just as much as grain, yeast, or hops. For example, if you were making a sweet style like Scottish Ale or even a Hefe, it might not be a good idea to go low on the IBU range AND target a malty/sweet water profile - or maybe, like me, you like that kind of thing. The point is that this opens up a lot of options for you to play with, but at the same time is also means there is more room for error, and acceptably so.