However I am curious if part of the path of Buddhism is to ultimately remove all emotions that one may have towards objects that bring happiness, replacing it completely with the happiness of love and compassion. Or can one live with both as long as they have the insight to not exaggerate feelings towards objects that bring happiness thus minimizing afflictive emotions?
The Dalai Lama commented on this in his book "Healing Anger", he said:
What premises or grounds do we have for accepting that mental afflictions can be ultimately rooted out and eliminated from our mind?
In Buddhist thought, we have three principal reasons for believing that this can happen.
One is that all deluded states of mind, all afflictive emotions and thoughts, are essentially distorted in their mode of apprehension, whereas all the antidotal factors such as love, compassion, insight, and so on not only are undistorted, but they also have grounding in our varied experience and in reality.
Second, all these antidotal forces also have the quality of being strengthened through practice and training. Through constant familiarity, one can enhance their capacity and increase their potential limitlessly. So the second premise is that as one enhances the capacity of these antidotal forces and increases their strength, one is able to correspondingly reduce the influences and effects of delusory states of mind.
The third premise is that the essential nature of mind is pure; in other words, there is the idea that the essential nature of mind is clear light or Buddha-nature.
So it is on these three premises that Buddhism accepts that delusions, all afflictive emotions and thoughts, can be ultimately eliminated through practice and meditation.
So we practice cultivating the antidotes to these afflicitive emotions, which minimizes them as we practice. And as the practice progresses, they become lessened and lessened and lessened, until the point that they are lessened so much, that they disappear entirely. But that does not necessarily mean that all emotions disappear entirely. It's just that the emotions are no longer "an affliction" that cause suffering. So to answer your two questions above, it's really not an either/or type of situation. I would say the answer is yes to both, minus the "remove all emotions" part.
'm sure this may be a question that has differing opinions, but when currently lacking a teacher to assist in the start of the journey, well, where does one start? Or to be more precise, is there a particular, thing, such as practicing meditation, that should be the focus at the beginning?
I would say the place to start would be simply to familiarize yourself with the basic teachings, a good "introduction to Buddhism" books would cover the basics if you haven't read something like that already. And start doing breathing meditation. Many meditation teachers, regardless of the type of meditation they teach, like to start people out with breathing meditation as the first practice. It's very simple and also of great benefit. You really can't go wrong with simple breathing meditation. But, it's not really a beginners practice even though it's very suited for beginners. "Advanced" practitioners also practice this breathing practice because it's very beneficial for every stage along the path. The Buddha himself put great importance on breathing meditation.