Basil is a tropical plant, whereas most herbs are Mediterranean or UK natives. It needs heat and moisture, so on a windowsill not outside, and it won’t survive the winter.
I grow marjoram (oregano), basil (indoors), mint, Korean mint (actually an Agastache), Quilquiña, winter savory, bay, thyme, chives, sweet cicely, parsley, rosemary.
bay, marjoram, thyme, rosemary, parsley are available all winter. Mint, sweet cicely and chives regrow from roots/bulbs each spring, the rest need to be re-sown every year.