These are just my inexpert and very incomplete observations and views. I think there are many many ways to parse Protestant Christians so any typology is bound to be incomplete. However since you asked about different types of Protestants I'll give some views based on my own limited knowledge.
I think the division is actually three-fold within traditonally Protestant denominations: liberal, mainline, and conservative. In addition there are movements that extend across denominations and even outside Protestantism, such as Restorationism, Evangelicalism, etc. Anyway, I think this three-fold division corresponds to the three modes of thinking in society today: the post-modern, the modern, and the pre-modern, respectively.
(1) Liberal Protestants are heavily influenced by postmodern thinking, and so they tend to adopt the postmodern view that truth is relative and that the highest moral law is 'follow your bliss' and 'if it feels good do it', so long as it doesn't involve judging or harming others. This is personal religion at its finest (or worst), and extremely liberal Christians are basically not much different from postmodern secularists, so I think similar approaches to both are appropriate.
In approaching a very liberal Christian the first thing to realize is that they don't care much about your claims to truth. Reason doesn't engage them the way it does for modernists. Postmoderns see things in terms of attraction-repulsion rather than rational-irrational. For example claims that Orthodoxy is the one true faith are likely to be repulsive rather than attractive to these types, no matter how reasonable the claim may be.
What matters most is authenticity, and the gravest sin for postmoderns, apart from judgmentalism, is hypocrisy. Basically a postmodern, whether Christian or not, will only judge you based on how authentically you adhere to your own faith. Apart from that practically all faiths and lifestyles are acceptable, which is why liberal Christians generally embrace homosexuality, abortion, feminism, religious pluralism, etc. If you walk the walk and talk the talk, you will be judged authentic in your faith and therefore admirable. That being said, there are some limits on this open attitude towards authenticity. It doesn't apply if autheticity to one's faith inherently involves judging or excluding others, for example. Yes, it's complicated.
In my opinion, the best approach here is not to get into a debate, because they will just respond with, "that is just your truth, not mine". End of discussion. Rather the first thing you need to demonstrate is that you and others live your faith authentically. Then a postmodern may become curious enough to ask about it, and to the extent you display authenticity and a welcoming non-judgmental attitude, may be attracted. You must be like the light that attracts the moth rather than the wind trying to blow the moth to the light. Being very open and non-judgmental, yet honest and non-apologetic about your faith, is probably the most effective. Exposure is the path to conversion, so invite those postmoderns who seem interested to attend liturgy and meet the community.
Certain aspects of Orthodoxy may appeal to the postmodern more than others, and these you might emphasize in discussion. Here I would include Orthodoxy's exotic non-western image, beautiful liturgy, monasticism, the emphasis on real spiritual practice, its ancient roots, its conciliar as opposed to authoritarian approach to governance, its emphasis on spiritual mentorship, etc. Most of all, the presentation of the Church as a hospital, as a therapeutic method, should be appealing to this type. Doctrinally, Christus Victor will appeal, but generally one should emphasize the unique and authentic practice of Orthodoxy over dogmas, cannons, and such. There are also many things that a liberal Christian will have trouble with, particularly the claim to Truth as the One Church, the emphasis on spiritual obedience, the strict moral code, lack of women priests, teachings on abortion and homosexuality, etc.
(2) Mainline Protestants are mostly modernist in outlook. They tend to be steeped in the Enlightenment and so find historical biblical criticism, evolutionary perspectives, scientific explanations, and the notion of doctrinal and liturgical development to be acceptable. Doctrinally a modernist is likely to be a theistic evolutionist or take a figurative and mythic view of Genesis. Some (many?) modernists have real trouble with miracles, the idea of a personal Devil, traditional conceptions of heaven and hell, and so forth, however this doesn't apply to all. Generally modernists have real trouble with spirituality, preferring to see religion in moral or social terms. Unlike postmoderns, modernists appreciate the importance of reason and can accept the notion of absolutes. Therefore more traditional apologetics may work, as may a study of history. Whereas the postmodern self-image is based on authenticity, the modern wants to see himself or herself as being reasonable, rational, and scientific in his or her faith. However, like postmoderns, modernists tend to be very individualistic about their faith, but try to ground it in reason as opposed to subjective emotion. As a result, the mystical and ritualistic aspects of Orthodoxy may be a problem, as will the usual criticisms like veneration of icons.
I would note that there are really two strands within modernism, even Christian modernism - what one might call the rational and the romantic. The rational strand is conservative regarding the 18th century Enlightenment and tends to be classically liberal and capitalist. This type of mainline Christian seeks in Christianity affirmation for a modern capitalist lifestyle and materialism. Therefore asceticism will make little sense to this type. The romantic tends to look more towards the 19th century and may hold sympathy for socialist or even Marxist ideas. Romantics tend to see themselves as champions for the oppressed and downtodden, and so for them religion is primarily about morality and social action rather than spirituality. If you cannot demonstrate Orthodoxy's engagement in charitable activities or mission work, the romantic Christian modernist will not be attracted. Obviously you need to know which kind of modern you are dealing with.
(3) Conservative or fundamental Protestants are the most likely to hold strongly to the doctrines of the Reformation such as sola scriptura (sometimes more strongly than the original reformers). In fact I'd say that many mainline and liberal Protestants only have a vague notion of their own theology, so if you start off your critique of their beliefs by mentioning sola scriptura or other technical terms you may get a blank look. Perhaps the defining characteristic of fundamentalist or conservative Protestants is doctrinal knowledge and purity. In my experience many conservatives are very well informed of their beliefs and can defend them with scriptural support. If you want to approach a conservative you had better know Holy Scripture inside and out. Probably the best way to reach these people is by showing the gaps in their scriptural understanding, those verses that are often overlooked but which Orthodox can show present a fuller interpretation. I don't know, that's just my guess. Other aspects common to conservative types is a strong emphasis on supernatural reality, Creationism, and a tendency to define themselves in opposition to modernists. Though not all conservatives are anti-scientific, some are.
I think there are many people who are mixed types, such as liberal-mainline or mainline-fundamentalist. For example, while I am definitely steeped in the modernist mainline attitude when it comes to emphasis on reason and science, I have as I've gotten older begun to appreciate the more positive aspects of both the liberal and conservative perspectives. I appreciate the conservative emphasis on doctrinal purity and living fully the life in Christ, and I appreciate the strong liberal emphasis on spiritual autheticity. In Orthodoxy I see a fairly harmonious blending of all three approaches, so that a Protestant of any orientation will find elements of Orthodoxy appealing (and other things a challenge). The key to witnessing to a Protestant is really to know who you are dealing with, because within denominations you will often find all types present.
I await any and all critiques or additions, as I am not particularly confident that the way I've explained all this is accurate. My own experiences and knowledge are necessarily limited.
Sincerely in Christ,