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

Mercury - Mercury represents communication skills, marketing, calculative ability, younger siblings, hobbies, skills with hands, intelligence, quick decision making, logical thinking, youthfulness 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.

House Ruler - Besides these karaka things, Mercury & 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 those things 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 Mercury-Venus Conjunction - Prima-facie it shows someone really good with numbers and calculation as Mercury & Venus are both best friends, Mercury represents Calculation and Venus represents Wealth. So, this person can be very good at counting and may be working in Finance related field. It is most common to see these people in Banks, Financial Institutes, as CA/CS/ICWAs or in Stock Markets. Mercury is Business & Venus is Wealth, so any wealth related Business can be really good for them. Specially if this conjunction is in Virgo then it is almost sure that person will get into Stocks, Shares, Banks or Accountancy field. But there is little bit more to this conjunction. Both these planets represent Skills, Talents and Hobbies. So, this person can be very creative, skillful and talented. They can be very pleasant with their talks or speech and can earn through their skills or hobbies. Actually, if these 2 planets are in good dignity in 1st house, 2nd house, 3rd house, 5th house, 7th house & 10th house, then it shows that someone can gain through Media & Movies. They love travelling. They would love to speak or write about Love Stories. At the same time, as Mercury is flirtatious by nature, it shows someone who is very flirtatious in love matters. Even if they are not flirtatious but if break-up happens then these people won't cry and get depressed for over an year. Within few days, they will be over that break-up and will be ready for new relation. It is because Mercury is quick traveler and Venus is Love. So, they are quick to make switch from 1 partner to another. In some cases, it can lead to infidelity. Overall, this is conjunction of a very skillful, creative and talented person. 

Who will win the Conjunction? - Venus will. Mercury is a neutral planet. It changes itself as per the planet it sits with. So, with Venus, Mercury will be Desire, Luxury & Wealth Oriented. 

Dignity & Strength - 

This conjunction can work best when it is in Taurus, Gemini, Leo, & Libra. Here both planets will get creative environment to develop their skills and person will gain through his talents and hobbies, 

It can make a great Spiritual Author/Speaker in Pisces. Likewise, in Virgo person is surely to go into Financial field. 

In Aries, person may have technical skills. 

In Cancer, person may be good at nourishing and taking care of others. 

In Scorpio & Sagittarius, person will develop skills related to Occult and Higher Education. 

As Capricorn & Aquarius are ruled by Saturn, person will realize his skills and talents in later part of life,