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This is quite the complicated subject if this is your first go. This will be by trial and error. Luckily basil does not require strong fertilizer to grow well. They are pretty carefree. If you city water does contain softeners, then you will want to avoid this. Any water will do as long as it is not loaded with salts, such as softened water. Your bottled nutrients should contain a small amount of chlorine to substitute, should you choose to use bottled water. They actually use SOME of the chlorine present in water.

Now, in hydroponics, you will not want to introduce any soil into the system. A hydroponic medium will be best, such as hydroton, grow stone, or perlite. As for standing up straight, it grows so fast hydroponically, that it will not have the ability to stay upright for very long. You can either trellis, or do what I do, which is let it hang over the side.

This article will give you more information: https://www.gardeningknowhow.com/special/containers/hydroponic-gardening-indoors.htm

You may not find plants yet but can always find seeds at your local garden center. Here's an article with tips on how to grow basil from seeds:

https://www.gardeningknowhow.com/edible/herbs/basil/growing-basil-seeds.htm

If you aren't planning on collecting seed, you can plant different varieties in the same container. It is when you let the plants go to seed that pollen gets moved from one variety to another. If your intent is to collect seed, first know that hybrid plants don't come true from seed- will not be an exact replica - even if no cross-pollination occurs. To prevent cross-pollination, Univ. of Florida recommends varieties should be 150 feet apart. http://gardeningsolutions.ifas.ufl.edu/plants/edibles/vegetables/basil.html

Pollinators need room to move about so I'm not sure a bushier plant is better for them. I would cut back every other stem when flowers start to show. The trimmed stems will produce another flower but at a later time. This way, you have a longer season of pollinator heaven. For the basil, trim off the flowers when the petals drop; it will produce new flowers if you don't let the plant produce seed. Lemon balm and mint are garden thugs and will gladly take over and spread everywhere via underground roots/stolons. They might clamber over your other plants and shade them out. Fertilizing will only encourage this behavior. An inch or two of compost around the plants should be sufficient nourishment for your purpose. You'll have happy bees!

Those symptoms are the main signs of a fungal infection. This happens from soil that remains too wet for too long, and is not allowed to dry out thoroughly.

From here, it is easier to start over with basil. Curing it may be a bit tedious and the recovery will likely take longer than it would to grow a seedling to the same size again.

In the future, you will want to let the soil dry out COMPLETELY down to about 3 or 4 inches before watering again. You can check with your finger, or a moisture meter.

This article will help you to grow basil: https://www.gardeningknowhow.com/edible/herbs/basil/how-to-grow-basil-plants.htm

Basil need a lot of sunlight!
These links will help you.

https://www.gardeningknowhow.com/edible/herbs/basil/information-on-how-to-grow-basil-indoors.htm
https://www.gardeningknowhow.com/edible/herbs/basil/basil-watering-tips.htm