Which sociological theory is most effective in approaching social issues: the symbolic interactionist perspective, the functionalist perspective, or the conflict perspective?

Answering this question requires one to determine in what way they personally interpret the world. These aren't hard sciences, so it has some room for subjectivity (hence why they are defined as perspectives).
The functionalist perspective emphasizes the idea that society is made up of several social institutions working together. For example, family systems, school systems, business systems, and political systems are all cogs within a societal machine meant to promote social harmony. To approach social issues with this perspective is to deem some issues as "functional" or "dysfunctional." One potential problem when tackling social issues with the functionalist perspective is that this perspective is predicated on the idea that these social institutions are constructed for good, and it may be too lenient on possible malice amongst the institutions themselves because of a generalized hopeful outlook keen on maintaining the status quo.
The symbolic interactionist perspective is focused on the micro (to the best of its ability whilst still remaining within the realm of sociology). It focuses on individuals and how they interact within groups as opposed to focusing solely on the groups the individuals inhabit. When tackling social issues, one potential problem to come about with this perspective is its lack of help; the perspective provides too much specificity and individual interpretation to provide a social framework from which one can determine a conclusion.
The conflict perspective perceives the world as several social institutions fighting for power and influence. If a person is a Marxist or modern feminist, they may be inclined to perceive the world in this manner, as it heavily criticizes capitalism and current hierarchies by claiming patriarchal oppression. One potential problem when tackling social issues that may arise out of this perspective is too stringently (and unfairly) categorizing people into groups to perpetuate a dangerous system from which a hierarchy based on oppression may be created.

Sociological theories (also known as theoretical perspectives) are as diverse as theories in other disciplines. However, applying these theoretical perspectives together provides sociologists a wider lens in which to view societal issues. So, if we use the example of homelessness as a social issue that needs to be solved, we can then apply each of the following theoretical perspectives to it: the symbolic interactionist perspective, the functionalist perspective, and the conflict perspective.
The symbolic interactionist perspective (often called symbolic interaction) is rooted in the work of social thinker, Max Weber (1864-1920) and his ideas concerning rationalism, or how societies are built around the notion of a society founded on logic and efficiency instead of traditions and morals. Weber might note that homelessness is a symbol of the United States inability to adhere to the tenets of a capitalist society, and as such, has caused certain members of society to be homeless. Simplistic yes, but in this example, homelessness is seen as a “symbol” of a failing of the greater society.
The functionalist perspective, is named for Emile Durkheim’s (1858-1917) perspective that society is greater than the sum of its parts. Durkheim viewed society like a living organism, in that all the parts functioned together for the benefit of the whole. For a society to truly function in an efficient manner every part needed to work correctly. As this is applied to our example of homelessness it could be argued that because of circumstances like wealth inequality, or subpar social services, or a downtrodden economy an individual could become homeless as a result.
The conflict perspective (also known as conflict theory) was coined by Karl Marx (1818-1883) who viewed conflict as the primary driver of social change. He maintained that constant strife between the owners of the means of production (the bourgeoisie) and the laborers (the proletariat) is what propels and shapes societies. If we were to apply a conflict perspective to the homelessness example perhaps we as sociologists could deduce that homelessness is caused by large, monopolistic corporations laying off hundreds of thousands of workers every year in sake of the bottom line, thus consigning many to homelessness.
There is no sociological perspective better than the next. In fact, taken in concert, applying all three of these sociological perspectives will ensure that a broader social context is understood by all.

Modern sociologists apply three basic theoretical perspectives; the functionalist perspective, the conflict perspective, and the symbolic interactionist perspective in an attempt to develop theoretical paradigms for unraveling the impact of society on people, and vice versa.
The functionalism perspective maintains that a weak society is as a result of social problems. However, social problems are not a reflection of a fundamental fault in the structuring of the society. Social problems should be solved in a gradual fashion rather than far-reaching and sudden change. In spite of their negative impacts, social problems occasionally serve essential societal roles.
The conflict theory suggests that social problems emanate from fundamental faults in the society’s structure, which are based on gender, race, social class, and other factors. To eliminate or reduce social inequalities, far-reaching change is needed in the societal structure.
Symbolic interactionism perspective indicates that social problems emanate from interactions among individuals. In essence, problematic characters in the society have been noted to copy their behaviors from other people in the society
All the aforementioned perspectives explore the same problems in society, but in distinct ways. Thus, it is true to conclude that each of these perspectives is as effective as the other. A collective consideration of their views offers a more detailed analysis of problems in society than any single view.
FURTHER READING
Theoretical Perspectives | Introduction to Sociology. (2012, February 1). Retrieved from https://courses.lumenlearning.com/atd-baycollege-sociology/chapter/theoretical-perspectives/

All three sociological theories have the potential to be effective in approaching issues of society, as each of these perspectives define some part of the framework of civilization.
The symbolic interactionist perspective, introduced in the early 1920’s by George Herbert Mead, asserts that meaning is attached to symbols. A handshake, a wedding ring, written music, for instance, are all symbols that represent characteristics of society and can be subject to individual interpretation. These elements of society are defined by individuals and can be perceived as such, thus emphasizing that humans see themselves as society dictates.
Next, the functionalist perspective, introduced by Emile Durkheim, defines society as the sum of it’s parts. This perspective is based on how each institution works with the others to form an inter dependency necessary to sustain and stabilize society. This macro theory asserts that the “parts”, such as education, law, marriage/family, religion, division of labor, work together to meet societal needs and allow communities to provide for individual needs, thus society is cohesive and working as a whole.
Lastly, the conflict perspective, introduced by Karl Marx, holds that society’s evolution over time demands for competition to take place between different demographic groups where inequality may exist. For instance, differences in class, race, gender can dictate who is able to obtain the most available resources. This conflict and competition is essential for achieving what is needed for survival, as well as flourishing in society.
The first theory, symbolic interactionist, is considered a micro theory, and is necessary in defining how individuals interact and coexist in society. The other two, functionalist and conflict, are macro theories, which encompass different aspects of survival in society on a large scale. All three perspectives contribute to the different facets of social issues.

Each sociological perspective has potential to be effective, depending on which aspect of society is being analyzed.The functionalist perspective argues that the different aspects of a society are all interconnected and self-regulated to promote social equality. This view would be effective in analyzing whether social institutions are functional or dysfunctional, and how these institutions create or impair social harmony.The conflict perspective posits that society consists of power struggles between groups competing for limited resources, so it would be most effective for analyzing the source and effect of socio-economic inequalities and how social institutions create hierarchy.The symbolic interactionist perspective examines micro-level interactions to examine how interactions create meaning, and how this influences inter-group behavior. This micro-sociological perspective would be most effective for analyzing the sociology or social psychology of small group interactions, and not broad societal trends.