Things to look at [the most] for Synastry/Compatibility
The sun and the moon are very important for compatibility. In general, the sun is important in outlining a person and their identity & conscious personality, and the moon is important in interpreting a person's subconscious personality and feelings/emotions. The moon is also very important in giving a reason for a person's actions, thoughts and way of living, because it is their subconscious and it is or can be known as their soul. So how this plays a role in compatibility, is that a person's emotions and feelings show the most when they are in love and so if two people’s emotions get along well [trine, opposition, conjunction, sextile] then chances are high for them to flow on the same wavelength and feel a deep, mutual attraction for each other. It can also work very well if a person's sun is positively aspecting [trine, opposition, conjunction, sextile] the significant other's moon sign. More often than not, it actually works best when the person's sun is positively aspecting the other person's moon sign. This is because much like when we look at the sky and see that the moon is reflecting upon the sun’s light, a person's identity (sun) will shine and be able to reflect to the other person’s emotions (moon), allowing them to release their emotions easily because the other person is able to show them off consciously and with ease. So the moon illuminates best when the sun is reflecting something similar, and thus, there becomes a sense of comfortability and great compatibility.
Venus is already known as the planet of love, beauty and relationships so I won't dwell too deep, but I want to add how it can influence compatibility in a way that other planets or houses cannot. Venus is quite similar to the moon in that it deals with feelings and matters of the heart. But Venus focuses specifically on love and desires, not just any emotions. So, this means that Venus comes out the most to play when you're in love or have a desire, mainly for a person. So essentially, if two people’s Venus signs do not match positively, it can be hard for the relationship to be sustained. This is not to say that these people cannot be in a relationship and have a good relationship, however it can be a little bit hard to maintain it as the Venus signs are finding it hard to be mutually attracted to each other [because they are inconjunct or badly aspected]. Funny enough though, you will find that a lot of people or couples who have Venus in the same sign (conjunct) can be very good together, yet pretty toxic for each other. This is because this same sign is showing off both its good traits and its bad traits in this one relationship. The toxicity comes in where the other person will understand where that energy is coming from because they also have it, so they can find it hard to let go of their significant other. It is a mess, but somehow it works out most of the time because they love each other, and have deep lust and memories together.
The North node, surprisingly, plays a significant role in compatibility because it is a person's sense of direction for their life path, and ultimately where their life is going or based on until the end. More often than not though, a person will act like their South node because this is their safe space, their comfort zone, the life/way they know well. But the South node is the life you are trying to leave behind, so life will try to pull you towards your North node and try to tire you (or make you get bored) of your South node traits. So, in the compatibility sense, two people are more likely to be compatible if they have the same North node (or North nodes that positively aspect each other [trine and sextile]) because their life path or sense of direction involves the same energy or way of living while leaving behind things that are also pretty similar (opposite to their NN).
We don't talk about Juno enough for compatibility, yet it is a very, very, very important placement. Juno (in dictionary form) is the asteroid that rules of marriage and commitment. Basically, what it is really, is what you deeply and truly look for in a partner in the standard of a long-term relationship/marriage or what you would like marriage to be like. So, for example, a person with a Juno in Sagittarius would be seeking or deeply desiring a marriage or a long-term relationship that is full of fun, freedom, adventure, conversations, and thrills. If it dies down or becomes boring, they can become a bit weary and seemingly bored, and so if the significant other doesn't really keep the relationship a lil fun and free anymore then they may stray away or end it. Another example would be someone who has a Juno in Aquarius; they would look for a relationship or marriage that is quite chilled and cool, yet bizarre/unusual and out of this world and full of mentally stimulating conversations or activities. They would not want something that is boring, predictable or uninteresting, unless there is a tactical reason behind it [lool]. A person with a Juno in Taurus on the other hand probably would prefer something quite predictable and relaxed and (seemingly) boring, because they enjoy the routine and stability of it. Thus, Juno does play a big role in synastry and if you want to know whether you’re compatible with your significant other in the long run.
For houses, the 5th, 7th and 8th house play the most roles in compatibility.
The 5th house is there for the romance part and it mainly comes out at the stage where two people are still dating, getting to know each other, being playful and finding out each other's interests and whether they are compatible or not. The 7th house, as we know it, is the house of relationships and partnerships, so it's essentially how a person is when they're in a union or being together with a person one on one. So, for example, whilst a person can have a Capricorn ascendant, they do have a Cancer descendant, which can make them a bit softer in relationships. This can also mean that if they are with someone who has, for example, a Scorpio ascendant, in the real world their risings may make them both come across as powerful, respect-seeking people and this can clash for both of them because they both want the power, but their descendants then make them have a more calmer, stable, ‘homey’ and loving union, so they end up being great together. Then the 8th house plays the role of shared finances, inheritances and things to come out of a marriage (if two people end up being married). It can also rule how a person acts towards another person's possessions and habits. This is more one sided, meaning that two people’s 8th houses do not have to be compatible, but if a person wants to learn how their significant other will be in the future of their marriage or long-term relationship then they could understand that through the 8th house. Lastly, the 8th house is also known as the house of sex and intimacy, so what they enjoy or how they act during sex is influenced by their 8th house [as well as their Rising (because the rising is how you act in every aspect of your life, aka your eternal mask) and Mars (the planet of movement & action)].