The issue of compatibility is not an easy one and is highly subjective. Much depends on compatibility for what purpose. Most web based sites are geared for the obivious him/her romantic relationship. This is not particularly helpful if you are concerned about your compatibility with your line manager.
Moreover compatibility in a short term romance is different from compatibility in a long term marriage - challenging aspects and issues may provide the drives to ensure that the union lasts and always has new areas to explore. The use of houses and house rulers may help to overcome this problem but it won't get rid of it.
People's idea of what makes compatibility, even in an agreed area, such as marriage, differ. So two Astrologers faced with the same chart may arrive at different conclusions because they see compatibility in different ways. The same applies to psychologists, marriage guidance counsellors, and other professions. At a limited level the following is typical - if one person is mainly Air and Water and the other is mainly Fire and Earth are they compatible? Some might argue obviously not, others might argue that together they form a balance whole.
To try and answer your question directly - if the relationship was just starting out I would look for romantic compatibility - Venus, Mars, Fifth House and ruler ruler, Sun, Moon Ascendants and possibly third House and ruler (ability to comunicate).
For a marriage far more is important - the seventh and its ruler, the eighth (resources of the marriage) and its ruler, definitely the third for communications, also the fourth and tenth - family and career can be important factors. If both have successful careers is one prepared to let the other's career take precedence? Career clashes can lead to marital breakdown.
No chart or interpretation can say whether a particular relationship will or will not succeed as a fact. Chart interpretation can give an indication or probability that a relationship will succeed.