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.

Jupiter - It is the most benefic planet and it represents all the auspicious things like Knowledge, Wisdom, Law, Guru, Spirituality, Religion, Philosophy, Literature, Elderly People and Children etc. For a girl, Jupiter also represents Husband.

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 too. 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, Jupiter & 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-Jupiter-Venus Conjunction - Common significations of Jupiter-Venus are Wealth, Knowledge, Teaching and Relationship. As Jupiter & Venus both were teachers, knowledge is common for both although Venus is normally seen as a relationship oriented planet.Likewise, Venus's highest representation is Service & Devotion and Jupiter is normally seen for spirituality. So, another common signification of Jupiter-Venus is Spirituality. Now, all these common traits of Jupiter-Venus are getting connected with Sun, which is soul, career and authority. So, this looks like a good conjunction for professional life. Normally, these people can be seen as very wealthy people and in good authority in public life as Jupiter is expanding traits of Sun & Venus both. They can be very knowledgeable and learned too. They can have a definite interest towards spirituality. Looks like a dream conjunction but wait a minute. Venus is with its 2 enemies Jupiter & Sun. So, it shows a person who can be very egoistic about his knowledge or wealth and that may spoil the relations. So, this conjunction sacrifices relations of person for other achievements in life. If Venus is combust then it is almost sure. If Jupiter is combust then person can have ego battles with teachers or problem in finding right teacher or his teacher can be very strict. If both are combust then all the good results of this conjunction, as stated above, will be delayed till 30 at least. In those situations, even if person may have wealth through inheritance, he may lose it due to his egoistical ways. At the same time, this can make person very creative. 

Who will win the Conjunction? - Venus is getting impacted by both Sun & Jupiter. So, it depends on the dignity between Sun & Jupiter to decide who rules the conjunction. Whichever planet is in better dignity will have more say in conjunction. 

Dignity & Strength - 

This conjunction is best in Pisces and Sagittarius as all 3 planets will be in good dignity.

In other signs, at least 1 planet will lose its strength and it depends on which planet is in better dignity or which dasha is running to interpret the impact or result.