@SoulFaith
In hindsight, I missed the context of your question in your original post and its intent, and I apologize for that. Whereas your question seems to relate to how we need to guard our hearts when it comes to potential suitors, my original answer relates more to how our hearts should be open to those we are seeking to help through the ministration of the gospel. I will get to your question and its actual intent in a moment, but first I would like to address what you said here:
When Jesus said that we need to be wise as serpents and harmless as doves, he was speaking to his disciples, whom he was sending out to proclaim the gospel. He warned them that they were being sent forth as sheep among wolves, and therefore they needed to be wise as serpents, or not ignorant of Satan's devices, while remaining harmless as doves, with the dove, in my understanding, referring to how the Spirit descended upon Jesus in bodily form like a dove. This contrast, in my estimation, relates to how God's Spirit ought to manifest in our lives in a harmless manner because we should be seeking the betterment of those with whom we share the gospel whereas Satan, that old serpent, and his children will vehemently and often violently oppose us in the same manner that a wolf seeks to devour a sheep. This is how I personally read and understand it.
To your point or to how we ought to guard our hearts when it comes to the topics of dating or marriage, I think that we are given the blueprint for that in what Paul wrote in the closing verses of Ephesians chapter 5. For the woman, she ought to be asking herself, "Does this man love me in the same manner in which Christ loves the church?" If the answer is "no," and in today's world, it frequently is, then she should avoid such a man like the plague. For the man, he ought to be asking himself, "Does this woman reverence me like the church reverences Christ?" Again, if the answer is "no," and in my particular case it always has been, then he should similarly avoid such a woman like the plague.
Personally, as a man, I focus on trying to be like Christ in my dealings with women. Really, in my dealings with anybody, but we are specifically talking about the context of male and female relationships now. Because of my giving and caring nature, there have been times when it initially appeared that there was some time of genuine connection between me and a woman, even within the context of just being friends. However, I eventually wind up walking away out of self-respect. In other words, I eventually conclude that the woman does not really respect me. Instead, she is just availing herself of things like my kindness and loyalty with no real regard for me, the person. Sorry to get a bit personal there, but I obviously am better equipped to answer this question from a man's perspective than a woman's perspective. For you women, yes, you should hold any man you are contemplating dating or marrying to the standard of Jesus. Granted, no man has attained to the fullness of the stature of Christ yet, but it ought to be rather obvious whether he is genuinely pursuing that standard or not. If he isn't, then run for your lives because he will ultimately selfishly use you as opposed to selflessly loving you.