It sounds like you think you are going to fail at choosing a church. Like anything, if you think you are going to fail, most likely you are going to fail.
A church is a family. With many problems and differences like any other family.
What was the Church like in the 1st century?
I don't see it any different than today.
1) Jews and Gentiles had their diffences. How to achieve equality, Romans 15:27
They were pleased to do it, and indeed they owe it to them. For if the
Gentiles have shared in the Jews’ spiritual blessings, they owe it to
the Jews to share with them their material blessings.
2) Divisions in the church. 1 Corinthians 11:18
In the first place, I hear that when you come together as a church,
there are divisions among you, and to some extent I believe it.
The church met in houses back then. Can we imagine the level of proselytization between them?
Arguing and persuading the people and one another as to what house to go to for communion.
Primary, at Church is where you partake in the Holy Communion. So, one thing to consider when choosing a house church. Proverbs 17:1 NET
Better is a dry crust of bread where there is quietness than a house
full of feasting with strife.
However, they were together in one mind. They knew that each house belonged to one church. And the church had the name of the city.
The apostles would reference them as a whole. i.e. Church at Jerusalem, Church at Antioch, Church of God, etc.
What does the Bible says about membership between churches?
It doesn't. Not in terms you are talking about in your question. There is only One Church of Christ Jesus.
Who is a member of the church according to the Bible?
Who ever has the seal of the Holy Spirit. Ephesians 1:13 NET
And you also were included in Christ when you heard the message of
truth, the gospel of your salvation. When you believed, you were
marked in him with a seal, the promised Holy Spirit.
Catholicism believes in the One True Church. All the Catholic Churches in the city are part of one whole church. Membership can be about how active you want to be.
Protestantism believes all the protestant denominations are part of the Universal Church.
You can go from placing membership from one church to another and yet be part of the Universal church. But membership can be a matter of salvation.
Good luck at choosing a church.