I am sorry for the reason you found your way here. It is really unfortunate, but on the orher hand you came to the right place to find answers. Most answers wil lcome in due time, there really is no point in forcing anything or getting ahead of yourself.
You said the separation was out of the blue and that your wife gave you no prior warning. I would venture to say that she did and that you just did not pick up on the clues. This to will crystalize in time as hindsight is always 2020.
I also find ti curious you calling yourself a man of faith, yet you seem ready to marry again. Is it not "till death do us part"?
You have been thrusted on this journey of selfdiscovery, obviously not by choice, but by circumstances. You have no other option but to continue walking and growing.
It is my firm opinion that you played your part in the demise of your marriage. Weather it was 10% or 50% or 80% is not all that important right now. What is important is that you contributed to the demise.
It is totally wrong to try and convince your wife to attend councling sessions, she will only resent you further. Right now you must give your wife time and space to perhaps start to miss you. But you must not keep standing still, you must move forward and grow. She might notice your movements and she might be tempted, but do not spoil it by contacting her or trying to have relationship talks with her. Her leaving is ample proof of that. Limit your interactions to children and finances and only if/when necesarry. From your posts it is evident that the children are old enough to maintain communication themselves.
Also do not badmouth your W to anyone and I mean anyone. The truth will surface eventually.
Do not go on a hunt for a wife number 2, you are waaaaay to damaged to think clearly now. Damaged attract damaged and you might attract someone in your life that is just as damaged if not more. You need time to heal and you need time to recover. Prior to 2 years of single life do not even attempt to date, you have to learn to be content and happy to be by yourself. Thinking that some else will bring joy to your life is a receipe for disaster. The only way you can be happy if you find happiness from within.
So immerse your self in work, your hobbies and kids. You are in for a looooong haul.