As a Christian, should we follow the Ten Commandments or the 613 laws?

No, neither of them. We no longer have to follow the Ten Commandments or the 613 laws. This is simply because Jesus did it for us.
But this does not mean that we have nothing to do, or that we no longer have any reference base.

Matthew 5:17   “Do not think that I came to destroy the Law or the Prophets. I did not come to destroy but to fulfill.

Jesus said that He came to fulfil the whole law. He did this so that we could have access to the same accomplishment, because it was simply impossible for us. Following the ten commandments or the 613 laws of the old covenant is impossible, no one can do it. That's why Jesus did the job for us.
It is therefore a waste of time to try to put into practice the ten commandments and/or the 613 laws of the old covenant.
Moreover, this would put us in a situation of permanent failure.  God has done much better than that.

This is what James says:
James 2:10   For whoever shall keep the whole law, and yet stumble in one point, he is guilty of all.

This shows us that if I want to live by the commandments and the 613 laws (because they are inseparable), then I have only two options:
- I have to be perfect to follow them all without any exception.
- I must admit that I would never be able to do it 100%, because the Bible tells us that 99.9% is not enough at all. It's 100% success or nothing.

It is easy to see that it is the 2nd option that is the only one possible.
In this case I realize that the law must be fulfilled so that I can be saved. I can't do it on my own. So I need someone perfect who will do it for me and who will agree to give me the opportunity to reach this level of holiness by giving His own life for me.

Of course Jesus did it!
It is very important to understand what happened in this achievement.
There is no question for me of trying to follow the law in the ten commandments or in the 613 laws given. Nor is it a question of trying to live like a Jew thinking that it will make me more spiritual. That's not what Jesus allowed me to have. This is not the opportunity that Jesus acquired for me on the cross.

Galatians 3:28   There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.

Colossians 3:11   where there is neither Greek nor Jew, circumcised nor uncircumcised, barbarian, Scythian, slave nor free, but Christ is all and in all.

Speaking a few Hebrew words, trying to follow easy laws that suit us will not make us more spiritual beings.

To try to fulfil the law of Moses is to want to be perfect and to be sacrificed on the cross! For only Jesus could accomplish this. If then I pursue the goal of fulfilling the whole law, then I position myself as a perfect saviour, whom I will never be.

Jesus did much better than that....

When we go through the new birth the Bible says that God comes and engraves His law in me.

2 Corinthians 3:3  clearly you are an epistle of Christ, ministered by us, written not with ink but by the Spirit of the living God, not on tablets of stone but on tablets of flesh, that is, of the heart.

The Spirit of God comes into my spirit to dwell there permanently.  His law is engraved in me, in my spirit. (For more details on the spirit see my study: spirit, soul and body).
This is often where the majority of Christians stumble. They do not understand why God would have put His law in us, and at the same time that we could have thoughts and bad deeds.
As a result, they tell themselves that they must then follow the law as a burden that they will carry all their lives, in order to do something on their own. So they mix law and grace. They live in Jesus, try their best to have a life without too many sins, asking forgiveness when they realize it, and reassure themselves by trying to make every effort to follow some aspects of the law.

Jesus gave us the fulfilment of the law, so it is no longer necessary to try to fulfil it.
Would that mean that we are free from the law and that we could live as our flesh would lead us?
Certainly not!

When Jesus comes to me through His Spirit, I am then engaged in a personal transformation to become more and more like God. Jesus said about it:
John 13:34  A new commandment I give to you, that you love one another; as I have loved you, that you also love one another.

Matthew 22: 37-40  Jesus said to him, “‘You shall love the Lord your God with all your heart, with all your soul, and with all your mind.’ This is the first and great commandment. And the second is like it: ‘You shall love your neighbor as yourself.’ On these two commandments hang all the Law and the Prophets.”

It is this law that God has engraved in our spirit. Our concern is therefore to love God with all the consequences that this implies, but also to do the same for my neighbour.
Today, therefore, I must first of all make a point of understanding what it means to love God (because not everyone has necessarily understood it well), then not put it into practice, but make it my way of life. Thus I would be able to do the same with my neighbour, so I will carry out by my life, a fulfilment of the law through Jesus Christ.

The whole law without any exception of a commandment or a rule will depend on these two things.
I am then engaged in a transformation of my person in order to accomplish this more and more effectively.
Of course, it could happen that I miss it, that I don't behave as I should.
Then in this case there is no need to go and try to fulfil certain rules of the law, or to try to find forgiveness from God, for it has already been given to me. Jesus came to abolish sin.

Hebrews 9:26  He then would have had to suffer often since the foundation of the world; but now, once at the end of the ages, He has appeared to put away sin by the sacrifice of Himself.

In this case, God will not impute your sin to you because sin is abolished at the cross.
This is a perfect barometer when I realize that I sin, it is this love that I have for Him that pushes me to sin less and less. That's how I get better and better to become like my father. This is how I must fulfil the law at my level in this period of grace in which we live.

The written law no longer concerns me, but the law engraved in me is the one that dictates my life.
Therefore I will sin even less effortlessly out of love than I would have done if I had tried to do it with all my strength by following a commandment.

Bye for now.