Let's 1st understand what these planets represent on their own?

Sun - Sun represents Soul, Personality, King, Government, Father, Authority, Career, Top Positions, Ego, Self Esteem, Health, Education etc.

Moon - Moon represents Mind, Emotions, Mother, Local Government, Peace of Mind, Home Environment, Water, Milk etc.

Venus - Venus is Beauty, Desire and Love, Liquid Money. Venus is the main significator of marriage. Venus represents girlfriend or wife for a man. Venus is the significator of all relations, may it be husband-wife or mother-daughter. Philosophically speaking, Venus is also the cause of all the sufferings in our life. How? Because Venus represents our desires and we get pain and suffering in our life only when our desires are not fulfilled.

3 planetary conjunction - Whenever 3 or more planets are conjunct with each other in a house/sign then things related to that house/sign become a kind of life focus for person. It is because of huge accumulation of energy within 30 degrees of sky. It means not only these 3 planets' energy is going into this house/sign but the energy of at least 4 to 6 house/sign is going into this house/sign as these planets will be ruling some houses in chart. So, this house/sign with conjunction becomes almost the most important house in chart. During Career Consultation, I give a huge importance to any such house which has 3 or more planets in it.

House Ruler - Besides these karaka things, Sun, Moon & Venus will also rule some houses in your chart and will represent things related to that house. Of course we can't cover conjunctions Ascendant and house wise else it will never be over. So, you have to include things related to the houses at the time of interpreting this conjunction. Also, we need to keep in mind all Yogas and Raj-Yogas which their conjunction would be making to completely understand the conjunction. Here, we can only cover meaning as per karakas.

Meaning of Sun-Moon-Venus Conjunction - This shows a person who is very much desire oriented as Soul (Sun) & Mind (Moon) are getting connected with Desires (Venus). This person may like to live a very convenient, wealthy and luxurious life. They may be all about fulfilling their own desires and may have a "Me-First" approach. Whether such a desire will be fulfilled or not depends on the dignity of planets and dashas. It also shows someone who is very creative and may follow his creative pursuits in life/career. They can be very good in wealth related matters. They can be relations oriented too and may not be able to find fulfillment if they are not in relation. But again, there me-first approach can spoil the relation. Again, it depends on the dignity of planets if they desire relation with a person or with a cause. As Venus's highest significance is service and devotion, depending on the dignity of Venus, they can find relation in serving others with devotion. Sun-Venus together makes relations suffer but person my be highly creative. Moon-Venus together makes person very emotional about relation but me-first approach hurts it. Sun-Moon together shows emotional repression. So, this conjunction can make person very creative and desire/service oriented but it may hurt the relationship aspect of life as Venus is with 2 enemies. If any of or both the planets are combust then we have to take the combust effect too. 

Who will win the Conjunction? - Sun will over-power Moon and Venus with its fire and heat. So, Sun is winning the conjunction. 

Dignity & Strength - 

This conjunction can work best in Sagittarius & Pisces as all planets are in good dignity here.

In Scorpio, all are not well placed. So, it can be termed as challenging position. 

In other signs, at least 1 planet will be in good dignity, hence results of the conjunction will largely depend on which planet is in better dignity in a sign, planets mutual impact on each other, as discussed above, and the dashas.