The tripartite agreement is specifically aimed at fresh graduates. You can sign a contract with the company before you get the diploma to prevent both parties from defaulting during this period. After signing the contract, you must go to this company after graduation. Although it is not as formal as a labor contract, it still has legal effect. If there is an agreed penalty at the time of signing, the breaching party must pay it. The tripartite agreement is very important, which can be used for file transfer and household registration after graduation, and once signed, it is not easy to go back on our word, so we must find a suitable job and sign it again.

The company won't sign a labor contract with you until you get your diploma, so this is your internship before graduation. After graduation, you need to find a company to sign a labor contract with you. The Labor Contract Law stipulates that a labor contract must be signed within one month from the date of employment. Many companies will have a probation period, which is included in the labor contract period. After the probation period, they can become full members.

Therefore, the order of the three is: signing a tripartite agreement (before graduation), signing a labor contract (after obtaining a diploma), and becoming a full member (after the probation period stipulated in the contract).

I suggest you be careful about your career planning. Whether you are a teacher or looking for another job, you should think it over before signing a tripartite agreement. As for the internship, you'd better find something you like, and don't delay to find a job. You said yourself that people don't necessarily want you after the internship, but you don't like it. Even if people want you, you won't necessarily stay, but you will delay finding a better job.

Attend more job fairs, give yourself a chance to choose, and sign a tripartite agreement after finding a suitable job.