Wow you are basically asking about water chemistry so this is going to be a long post, or several posts lol because I doubt I'll be able to get to it all at once!

Okay, first the easy one, which is household pH up/down products:
To lower pH in an emergency, the easiest and safest products are cider vinegar and natural lemon juice; acetic and citric acids, respectively. Now, these are ORGANIC rather than INORGANIC acids, and are also in the family of WEAK acids- they have a complex chemistry compared to the STRONG acids, and go into an interesting buffering equilibrium in your solution. Preferably, you would want to use a strong acid such as Phosphoric or Nitric to lower your pH- the H+ ion dissociates completely and acts to 'cleanly' lower the pH of your solution by acting on OH- ions that are present, and combining to form water, and a salt (from the N or P combining with whatever the OH had originally been attached to). This is a really oversimplified version lol.

To RAISE pH, you actually would want to avoid baking soda, which is chemically Sodium bicarbonate, and plants have a very low tolerance for sodium, so by the time you have raised your pH, you are already at a potentially harmful concentration of Sodium in your solution. Limestone is Calcium carbonate, and lime is a much safer additive. I have not actually tried this, but if your tap water is very acidic, you should be able to put some lime in it and shake it or stir it to try to neutralize some of that acid and raise the pH, but I'd let it settle after and pour off the liquid and discard anything that has fallen out of solution or suspension. Or get some pH Up...
The trick is to start with a soil mix that contains a natural buffer or pH balancer. Lime in your soil is one type of additive; others are -oddly- organic acids! Back to the buffering qualities of organic acids; there are some that buffer close to neutral, which functionally acting as an acid still. A common example of this is Humic acid, which you will find in the mineral Leonardite, in composted leaf litter (humus), and in many good fertilizers and additives like Pure Blend, Canna Bio, TopMax, Soil Syrup, and many many others.

Okay next subject: Your tap water 'killing micronutrients'. Well, if that was the exact wording he used, he is sadly underinformed in this area. Micronutrients are by definition trace amounts of metals that your plants need- at very low levels!- such as Boron, Magnesium, Zinc, and others. They are inorganic and cannot be killed. They will often be added to fertilizer as their Phosphate salt if it is soluble (the format being for example Magnesium phosphate), or chelated by an ion such as Oxalate or EDTA. Chelation means making the metal unable to interact with other things in your solution and become harmful to your soil environment. Chelators are important components of 'flsuhing' or 'clearing' solutions. Humic acid, among its other cool properties, is a valuable chelator! I have been known to flush my plants with a very weak solution of Humic acid.

Back to what Hydro Shop Guy is on about... Tap water contains chloramine, which will kill bacteria if the concentration is high enough. This could be an issue for you if you are running a pure-organic grow that depends heavily upon a living soil with bacteria, fungi, and other microorganisms in it, breaking down your organic fertilizers into components that the plants can actually use. If you have a highly treated tap water, organic growing may be difficult for you. Chloramine may be removed with activated carbon- you can set up a 5 gallon pail with a fish tank filter of the sort that has the hand-packed charcoal chamber, and let it run overnight to drastically reduce the concentration of contaminants in there. I don't know how much water can be treated by a specific amount of carbon, and it depends also on particle size of the charcoal and concentration of chloramine in your water.

Water sources pros and cons:
Tap- 'Tap water' is a pretty broad term and can mean anything. I'll assume you mean 'city water'. It's usually at an acceptable pH and hardness, but may be TOO hard and sometimes has high levels of disinfectants in it. It may be difficult to use for hydroponics, especially if it is 'hard'. Check your sink for evidence of 'lime scale' for a quick diagnosis that yup, it's way too hard.
Bottle water- Bottled drinking water often has too much sodium in it, and it's expensive. Not my choice.
Distilled water from any source- Actually a pretty good choice, and if your AC or dehumidifier has a plastic, not metal, receptacle, you might even be able to use that as distilled water (depends on the condition of the coils and if they are leaching off metals into the water as they condense it). Distilled water is predictable. You have to add calmag plus to it, up to ~200-300 ppm, and then check the pH. It should come out correct after addition of your calmag.
RO/reverse osmosis- Great stuff, better quality than distilled, more predictable even; again you have to add calmag.
Creek or stream water- Where does your stream come from? Look upstream. What is the landscape like? You can end up with serious issues. I'd avoid it in general; it's just too unpredictable, and subject to rapid changes with weather events or upstream releases.
Well water- Again, it depends on where your well is located. I had SERIOUS problems at a location where the well water was loaded with organic acids, and even though it tested a perfect 7.0, it used up all the lime in my soil in like 3 weeks and killed a crop. lol. Gotta love how Nature outwits us no matter how smart we think we are!

A final note on pH, ionic strength, and calmag.
RO water has an ionic strength, theoretically, that approaches ZERO. Any pH readings on pure RO or distilled water mean NOTHING! Unless you have a research-grade pH meter (you don't, I promise!) that can actually read solutions where the conductivity is close to zero, don't even bother! Read your pH AFTER you add the calmag and create your perfect 'imitation tap water'.
Most pH meters we all have are designed to read HIGH ionic strength solutions. This means at the fertilizer or waste water level. Imagine you are looking at a city from high up in the air. You can barely make out individual people walking around. Now imaging that all the people are standing close together in a crowd. Now you can see that there are actually people there! That's sort of the idea. Your average pH mater can only see and measure the crowd.

Okay that's enough of that for now. I have to go play with Phosphate buffers and dialyze some proteins!