This may seem a silly and basic question to some, but how exactly do you know which sins are more serious than others?
As a Christian I don't really think much in terms of some sins being more serious than others.
Sin is violation of God's law, which according to Jesus in principle rests on love for God and neighbour as yourself.
So whether that is, say, lying to your girlfriend about something or committing genocide, both fail the above principle.
Some sins are more wide ranging in their devastation though. For example sending 6 million Jews to the gas chamber obviously hurts more people than swearing at your brother does, even though both are unloving and unacceptable.
A little sin can have a big rebellion behind it.
It seems that all of the ten commandments are considered equal, but are these less important than the seven deadly sins? Or some of the old testament rules still followed or various other example in all parts of the Bible where moral lessons are taught.
The Old Testament included some rules for theocratic statism and ceremonial regulations and a sacrificial system that are redundant today, because we are no longer BC but AD. I no longer sacrifice a goat, for example, because the point of that was a symbolic reminder for the Jews thousands of years ago of their future Messiah who we now know was Jesus.
Sin isn't just a list of rules, it is again violation of that principle which demands love for God and neighbour as yourself. For example, thou shalt not covet thy neighbour's ... ass. Well unless you want to talk about an ass of a totally different kind, well a lot of us don't have asses these days, but the principle is still there, you know what I mean? That was an example to show them their sin back then, so that they'd understand their need for God's grace, help, forgiveness, and so on.
Humans have a real problem with not loving God and their neighbour as God's law demands. Jesus fulfils those demands on people's behalves, so those who trust in him cannot be self-righteous and can instead be counted by God as good people, etc.
Is it basically up to your own judgement? Or is there a grading system shown in scritpure itself to guide people in a clear way?
I use my conscience as the Bible has affected it.
Not everyone has the same conscience, for some people there are things they can't do that I can, such as drinking, that are not forbidden by the Bible. But when a Christian friend of mine does something like fornicates, I try to show them relevant Bible stuff to persuade their conscience and get them to repent.
Hope that helps.