The Rambam (Issurei Biah 13:4) identifies three things which the convert seeks in joining the Jewish people.
1. To join the covenant
2. To find protection under the wings of the Shechina (divine providence)
3. Accepting the Yoke of Torah
These three ideas are the basic features of the Jewish people. The first is Jewish identity; being part of the Jewish people going all the way back to Avraham; of being in a national relationship with God. A national identity of rejecting idols, and living an ethical life of justice and righteousness. The prospective convert is seeking to be part of this Jewish destiny. A destiny of closeness to God, but which frequently carries with it oppression by the nations of the world.
The second is seeking a relationship with God. The convert recognizes that divine providence is in direct proportion to a person’s knowledge and focus on God. By joining the Jewish people, he seeks to live under the governance of divine providence.
The third idea is serving God. Through the Mitzvot all of one’s actions are under divine authority.
While some Jews participate in only some of these three, a full expression of Judaism must have all three. A Jew must identify as a part of the Jewish nation, joining in their joys and suffering. A Jew must seek a relationship with God. And a Jew must live a life of commitment to mitzvot.
The Jewish people underwent all three steps in the process of becoming a nation (Issurei Biah 13:1-3). First, in Egypt we re-accepted the covenant with the “God of our fathers” through circumcising ourselves and our children in preparation for the Korban Pesach. Then at Sinai we purified ourselves in preparation for our encounter with God. Finally we brought Korbanot as part of the event of Sinai, ushering in a life of service to God through sacrifices, which serve as a model for all mitzvot.
Similarly, the court informs the prospective convert of all three domains, insisting that the convert accept all of them (Issurei Biah 14:1-5). Then the actual process of conversion is through the same three acts. First accepting the covenant with circumcision, then purification through immersion in a mikva (just like one preparing to enter the Mikdash), and finally bringing a korban.
However, while all three are necessary, there is a hierarchy among the three. The covenant and the mitzvot are subservient, but nearly indispensable, to the second, a relationship with God.
The covenant is about a relationship with God through our national history and identity. Much of our life is driven by our self identity, an identity which is heavily shaped by the groups we are part of. By identifying with a nation seeking God, that seeps into our self conception as well. Furthermore, human beings are social creatures. Without the support of a group we are likely to fail in achieving our goals. Our friends and compatriots in our quest to find God and to live a Godly life, provide advice and support and strengthen our resolve to carry out this mission in spite of the challenges. While simultaneously we help them in the same way. And without being raised with such an identity, most of us would never have found this path at all.
Similarly the life of Mitzvot is instrumental to closeness to God. As physical creatures we live in a world of action. Our behaviors shape our thoughts and character. Without the regimen of Mitzvot we would rarely think about God. Even if we were intellectually inclined and did think about God, we would live a bifurcated life. We would relate to God in our thoughts, but live according to our ingrained habits – including habits which are bad for society, and which bias our thinking. Whenever we do a mitzva, it is as if we were focused on God at that time, and can awaken thoughts and focus. Furthermore, many of the mitzvot are practice in good character traits, traits which are ingrained through repeated focused practice. While a person can develop their own regimen of practice, they are less likely to be successful. The Torah’s interpretation has been refined over generations by a community of wise practitioners. A personally devised system, even if it borrows heavily from various spiritual and ethical systems, will be limited by the person’s understanding and experience, which might be good on paper, but will lack the feedback of real world experience. Additionally, it is easier to maintain a commitment to Mitzvot which are experienced as a single choice to accept the system as a whole; while a personal practice needs a separate choice for each part.
Ultimately what the convert seeks, and what we should seek is to come under the wings of the shechina. But as Jews we are committed to community and commandments as the means to this goal.