I think that the right personality types that are compatible are ones that are similar but different in the same time. They cannot be the same type, since it will result in boredom and lack of growth in a relationship. If they are completely opposite, they will get in too many disagreements, won't understand eachother and probably won't get along.
I think you must look at your two main functions to figure out what is your ideal type.
for example an ENFP's two main functions:
Now, that means that its ideal partner should have at least one of those as their second function, but not as its main function!
So, the the ENFP's ideal partner must have:
either has their second function OR as their main function
examples: ISFJ, INTJ
the mirrors of the first main function, the mirror of the second function does not apply.
examples: INFP, INTP
Therefore, the ENFP's possible partners are: INTJ, INFP, ISFJ, INTP.
Using this system you can figure out what is your ideal partner for your personality type, though of course this is just speculation that I have thought of right now, so it might be completely wrong.
Anyways, everyone is welcome to post their thoughts on how someone can figure out their ideal type.