I'm growing 3 different types of Asian basils this year: Lettuce-Leaf, Queen of Siam, and Lime Basil. The Queen of Siam basil reminds me a lot of basil I've been served in Thai and Vietnamese retaurants. I personally prefer the Asian basils. The Genovese I grew once was too strong, overpowering.
I got my seeds from Baker's Creek
http://www.rareseeds.com
I have to agree that a variety of Spearmint is the mint usually used. It has a ruffley leaf, and reminds me a little of Applemint, (might be Applemint). As annietomatomad suggested, mint and basil both will root very easily. That is the sure way to make sure you grow the same thing.