It's lovely that you would like to surround yourself with your plants when you're out on your balcony.
They'll grow best and won't need much looking after if you plant them in pots with a water reservoir. This'll help ensure that they have a constant water supply. The size of the pots depends on the size and root system of the plant, as well as how thirsty the plant is. In summer, a hydrangea will easily require two litres of water a day, whereas a peony will be satisfied with half a litre; a datura can "swallow" up to three or four litres a day in high summer. If lugging a watering can around is too much for you, it could be worth finding out whether an automatic watering system would be a suitable alternative; all you need is a tap on the balcony.
When it comes to soil, I would recommend a high-quality soil with a high clay content. It's best to split the fertilisation process in two: Start with basic fertilisation by mixing a long-term fertiliser into the soil when you plant. Depending on the weather, add a small amount of liquid fertiliser (flowering plant fertiliser).
Lastly, to answer your question about how deep the soil should be: Plant the balled roots of the plants so that they are covered by roughly two centimetres of fresh soil.
If you've chosen a suitably sized pot, you will need to repot the plants every two years; for peonies, repot every three to four years.