Since I will not be making just pesto or Italian food, I was thinking of Basil Genovese. Or would sweet Basil be better?
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Pat is a trusted home cook.
I plant about 10 sweet basil plants every year and use it in everything. It's pretty hardy and all purpose.
I find Genovese basil to be the easiest to grow in a New England garden. It doesn't bolt too soon and it thrives under a variety of conditions. That said, I am also a fan of a variety called Fino, which has tiny leaves but big flavor and would do well in a pot. I always grow Thai basil, but it tends to have tougher stems and to go to flower more quickly. Check out the varieties in the online catalogs of Johnnys Selected Seeds or Fedco. (Lemon basil is nice, too. The purple varieties are ornamental but also tasty and beautiful in a salad.)
pierino is a trusted source on General Cooking and Tough Love.
Thai basil and African basil aren't true basil but they can be a bit hardier. The frustrating thing about growing basil is that you have to be watchful and pinch off the flower buds or else the plants will "bolt" and you will be left with leggy stems.
For Asian dishes, it's great to have a Thai basil plant around!