A few herbs grow on their own in my place (and some are pretty invasive) : peppermint, flat parsley, lemon balm, sage, thyme, oregano, savory, juniper.
I've added lemon verbena, chives, spearmint, curly parsley, rosemary, lavenders, coriander, basil.
I would love to grow ginger, though our climate is very dry. Maybe I'll try next year.
To help basil develop you can pinch the tip and it will divide and grow new stems.
I don't thing curly parsley tastes like flat at all, I think flat tastes much nicer and is more complex, slightly closer to coriander.