My question I suppose is, what personality type(s) are supposed to be compatible with me on a relationship level?
Well, one can always "join forces" with whomever you feel a connection to, no matter their personality type. So, it is also more flexible than many people would seem to think.
If you're a strong I, an ISTP with a weak I, might work wonderfully. Same with J/P. If you're a weak P though, the partner is recommended to be a J. Since most people are more on the middle of the spectrum, and not on either extreme, first and/or last letter is often said to be a good match. Two strong Es will for example be more likely to have trouble staying in a long relationship than two Es where one is on the border to be an introvert.
S/N is also recommended to be the same. For Ss, this rarely matters, but many Ns feel unfulfilled when in a relationship with an S, due to Ns need for "complexity" and "deepness". Sorry (not really), but we often find strong Ss shallow, unless they are a healthy enneagram type 2. Hehe
F/T works about the same way as N/S does, but it is far from as "crucial". Two Ts are more likely not to fight, and if they do, they will have a more similar way of trying to resolve the conflict.
Then again, I know this ENTJ who just can't stop attracting ISFPs. He loves them, and although he finds them irrational, naïve and often easily butt-hurt, opposites attract.
Enneagram, instinctual variants, socionics (subtype), mental health... There are a fuckload of factors in play when choosing a partner.
But yeah... ESTJ, ESFJ (what's often listed)...
How can I "seek" these people out? Are there signs or something I can look for?
Do loads and loads of reading. That way you'll learn the signs of Is, Es, Ss, Ns etc. by heart, and you can eventually spot it by looking at how they walk
My advise is to read up on functions and their stacking, as well as the letters of course, because the functions are, as you probably know, what the letters are based upon. Good luck!