Getting lowest three different items in same table with mysql

Hi guys…
I’m very new to these server-side things…
I have a little project which I’m coding in AS3 Flash… But I needed mysql and php for score recording…
My game has 3 levels, and it will show the user these 3 levels scores every time he/she logins… (Example = Your best scores : level1->20 level2->45 level3->62)

Now the score table has, one id column for recognizing the user, and the two others for game_type and score…
the table is like this :
id | score | game_type
1 12 0
1 23 0
1 32 1
1 46 0
1 55 1
1 78 1
1 18 0
1 71 2
1 47 2
1 13 2

What I want to do is, with one query, get every game_type’s lowest score…

For the above example : type0->12 type1 -> 32 type2-> 13

My query is this:
SELECT score
FROM ScoreTable
WHERE id = $userID AND game_type
IN (SELECT game_type FROM ScoreTable)
ORDER BY score ASC LIMIT 3

But I can not get the result I want…
Any ideas?

Thanks in advance…