Hello Scott, welcome to TFK!
You should not need to use bottled water, unless you have some known issue/problem with your tap water. If you tap water is chlorinated, you will need a conditioner to remove the chlorine/chloromine.
Byron is correct about weekly water changes although we might quibble about the amount. It is very important, even in heavily planted tanks to replace a portion of the polluted water with fresh water. If your tank has gravel, a gravel siphon removes unwanted and decaying detritus from down under. As to the amount of water, anywhere from 25% to 50% (so for your 10g that's 2.5g to 5g weekly).
It is also important to periodically service the filter. This may simply mean removing the filter media and giving it a good rinse in tank or conditioned water (you don't want chlorine to kill beneficial bacteria in the media). Depending on the bio-load, you may not need to do this every week.
A good measure to further increase water purity and have a more stable tank is a lot of living plants. Plants go a long way in not only helping to purify the water but also serve as an alternate food source and an excellent resting/hiding place for fish. Some plants may require more lighting than the average tank hood will provide. You should have bulbs that produce 6500k lumins. However, most floating plants do well (I like anacharis) under most all lights due to their proximity to the light source.
Also as Byron recommended, you don't really want or need to adjust for pH. The weekly water change should help stabilize the pH within an acceptable range.
You said you've been through a lot of fish - sounds ominous. Most folks new to the hobby are unaware of the nitrogen cycle and the beneficial bacteria that develop to oxidize toxic compounds...ammonia to nitrites, nitrites to nitrates and water changes to remove nitrates. Look in the articles section for Bacteria in the Freshwater Aquarium
I hope this helps in some small way and again welcome to the forum and keep us posted.
AD (Btw, I keep my tank in the living room!)