If I boil tap water in a clean pot, is it still necessary to purchase distilled water, or...?!

No, minerals are heavier than water (ie. won't evaporate). If you boil tap water you are going to end up with a higher concentration of minerals. Think about it. If you boiled a cup of lead and water do you think the overall composition would be a higher overall percentage of water or lead. Sorry, not the answer you were looking for, but here is the upside, you can use this knowledge to make the pure water you are looking for. When you boil water, the pure water turns to water vapor (a gas), if you can collect that, you will have pure water. What you are looking for is to boil tap water, and only save the evaporation, not the stuff being boiled. Place a small pot of tap water into a larger pot, with a metal (or pyrex) bowl upside down on it. When the water boils from the smaller central pot, the water vapor (pure h20) will recondense (turn back into a liquid) on the underside of the bowl and run down the side into the bigger pot. Ditch the stuff in the smaller pot and the stuff in the bigger one will be pure. You can even use a similar method to make drinkable water from urine (gross right, but if you are in a survival situation that is good to know.

Science

Boiling will, as you rightly said, kill the bacteria. However the minerals are ions that are dissolved in the water. To get rid of them you need a filter - a common one is the ion exchange column which is used in boilers and dishwashers. Most use common table salt (ions have charge and are attracted to the ions in salt).
Try searching for instructions for homemade exchange columns or buy a simple Brita water filter - comeas as a jug which filters water before dispensing.

Distillation is different than just being boiled. It is a process that removes all the minerals and other solids from water making it pure. Distilled water is good for use in applications where corrosion could cause problems like in a steam iron.
If you boil water it will be sterile but will still retain the minerals like calcium and iron.
Some people use distilled water for baby formulas, other uses are for canning where hard water can cloud the end product.

Depends on the reasoning for doing so. Can you elaborate?


Edit: I would say that you could pass it through a coffee filter, but seeing as you want to remove so much...just get the distilled water ( ps chances are, they will still be there to an extent)
Boiling will remove bacteria ...sorta

You can just put it in a gallon jug and leave it untouched for awhile ,, something like 48 hours, that you would have to google . but that distills it , by letting it sit .

why dont you just get a brita or a zero water pitcher with a filter , instant.

You may not buy some distilled water anymore,just leave the water you boiled for a couple of hours in a container then you may drink it.

http://www.thechocolategift.ca/

YES IT WILLL TAKE ALL THE GERMS OUT AND STUFF OF COURSE ITLL HAVE A LITTLE EXTRA BUT U WONT TASTE IT AND IT WONT KILL YOU AND ITS NOT BAD FFOR U AT ALL IM PRETTY SURE IT WORKS SO YES.

Its better to boil water specifically on a 30mins of boiling.

boiling will kill all germs im not sure if it's equivalent to distilled water though