Any very firm unripe green papaya can be used for the recipe, ranging from the small Hawaiian papaya to the huge Mexican variety.
http://www.thai-info.net/thaifood/somtam.htm
Green Papaya Salad Recipe -- ThaiTable.com
Som tum is an individual dish that you will find you might like your with more, say, lime juice than what the recipe calls for.
http://www.thaitable.com/Thai/recipes/Green_Papaya_Salad.htm
Som tam or Som tum is a spicy salad made from shredded unripened papaya. Som tam, the dish combines the four main tastes of Thai cuisine: sour lime, hot chili, salty fish sauce, and sweetness added by palm sugar.
Som Tam Pla Muk (Spicy Squid and Papaya Salad)
The squid, or pla muk, adds a nice meaty texture to this classic Thai papaya salad.
Ingredients (for 2 serves)
1 squid (280g), scored in a crisscross pattern then cut into pieces
5 small cloves of garlic, peeled
15 Thai chillies of assorted colours
1/4 cup French beans, cut into 1" pieces
1 3/4 tsp palm sugar
3 tbsp fish sauce
2 1/2 tbsp lime juice
1/2 cup grated carrot
1/2 cup grated green papaya
6 herry tomatoes, halved
2 tbsp fried cashew nuts, coarsely ground
How to prepare som tam pla muk
1. Bring a pot of water to the boil over, add the squid and boil until cooked through. Remove and soak in cold water for a moment, drain.
2. In a mortar, coarsely pound garlic and Thai chillies together. Add French beans, lightly crush. Add palm sugar, fish sauce and lime juice. Lightly pound and toss to combine. Add squid, carrot and green papaya. Pound and toss, and then add cherry tomatoes. Toss again to mix well.
3. Spoon onto a serving dish or bowl, top with fried cashew nut and serve at once.
credit: http://www.verythai.co.uk/pages.php?page=77
Som tam Tips
Buying a Green Papaya: You can try looking for a very green papaya at your grocery store (either 2 Hawaiian or 1 Caribbean type). But personally, I recommend buying one at an Asian store (as pictured), simply because it is difficult to tell whether a papaya is green or actually in one of the stages of ripening.
Asian stores and markets sell green papayas labelled as such. Sometimes they are even sliced open so you can see it is green inside (the seeds will be white).
Slice the papaya in half lengthwise and crack it open. Scrape out the seeds and discard. Then turn over each half and peel off the green skin.
You can either use a large-size grater to grate the papaya, or shred it as they do in Thailand (pictured here). Simply make many long cuts into the flesh, then thinly slice off the top layer into a bowl. Continue until all the papaya is shredded.
Any remaining pieces can be chopped up into strips with your knife.
Note that Thai cooks usually preform an optional step here, bashing the shredded papaya with a pestle to bring out the juice. Another way is to place half the shredded papaya in a food processor and pulse briefly. Mix this with the remaining papaya.
credit: http://thaifood.about.com/od/thairecipesstepbystep/ss/somtamrecipe.htm