I understand that, for Christians, they are saved by their faith in Christ.
But as I understand it, even so, they should still try their best to follow the law, commandments etc... though some of that changed around food and circumcision.
But what rules are Christians still supposed to follow to the best of their ability? Working on Sabbath? Making sacrifices? Are most of the Old Testament rules the ideal? etc.
Where is this set out?
It's a bit complex. We inherited much from Judaism, but in Judaism, there are many laws which are only for Jews, though there are universal laws and morals for everyone - Jews get those plus others. Christianity started among Jews, but the first generation of Christians was led by the Holy Spirit to understand that non-Jews can become Christians without having to follow everything that Jews have to follow (Acts 15). I do not take this as lowering the bar for Jewish Christians, but an acknowledgement that there are certain Old Testament obligations that non-Jews were not held to before the time of Christ, and that they are still not held to since the time of Christ. When people do not understand this backdrop, either Christian or non-Christian, they become confused about what should be allowed and what shouldn't be allowed.
A consequence of that is wrongly calling out negligence or hypocrisy or cherry-picking because they have the standards mixed up. In truth, this way of interpreting the Old Testament originated in Judaism before the time of Christ, and you can find it in the teachings of Jewish scholars - it wasn't something Christians made up in order to get by with less demands (though I can't speak for everyone who didn't know that). This parallels Martin Luther's sermon on how Christians should regard the Law of Moses
here. When Martin Luther and Jewish teachers both say the same things about the Law, I pay attention.
Now that we have establishing that lens out of the way, consider what is repeated from the Old Testament in the New Testament, and to whom it was commanded. The teachings of Jesus need to be followed, as do all commands given to the general church. If someone is from a Jewish background, uphold the Law by faith (Romans 3:31). If not, live by faith in the relative freedom you have, but again, obey the New Testament commands. Sin offerings of course, are out because Jesus is the once-for-all sacrifice for sins.
Yes, this is a bit vague, but there's no simple source that cleanly and neatly delineates everything. Scriptures have to be pieced together to get the answer you are looking for.
