Let me go ahead and break down the "unequally yoked" part of what the OP was stating:
In the New Testament, the Apostle Paul discussed in detail why Christians and non Christians should not be bound together in a marital relationship. The bottom line up front is that the OP is looking for someone who shares the same core value and belief system because it is her hope that one day she can find the one her Creator has for her.
Now let me break it down even further:
By having a similar core and belief system, as a couple, you could move forward together for the most part in making life decisions based on the fact that the two of you share the same common values and beliefs. It truly helps when your partner is on the same sheet of music, because you know that he/she has your back and will usually back you up in whatever decisions you make, good or bad. You will know that when something happens and it comes down to morals and ethics, that you and your partner will be able to make ethical and morally sound decisions based on your core belief system. Now don't get me wrong, there will be times in which both partners will disagree; it's not perfect or rocket science.
In a Christian relationship, it is Christ-centered, faith-based, and the basis for it can be found in Scripture. There are people out there, that despite not being Christians act more like them than believers. There are some men out there who claim to be Christians but push the physical boundaries more than nonbelievers do at times. I am one of the flawed individuals I just described above. In dating I was a total hypocrite, enough said.
But on the other side of the coin, to go back to the reasoning for having similar values and beliefs, I have also been on that side of the coin where I was unequally yoked for four and a half years. It was painful and a mistake I never vow to make again. In something unequally yoked, one person works harder than the other, keeps things together, etc. Imagine those ox working the field and one working and the other isn't? That is you literal and visual on how this expression works.
To the OP - I wish you the best of luck.
Randy