What a pain. I'm like you, I prefer things tidy and clean. Some people think like us, some people are in the middle, some people aren't too concerned and will let the mess pile up.
You are in the right though because having a clean and tidy home is a sign of integrity, of having self-worth, and now that you two live together, it's more important because it is a sign that he is willing to work for your relationship.
I suspect he hasn't given it much thought, but he honestly doesn't mean to upset you. He does apologise, so he does care.
Now that you have both consented to move in and live together, you should both be aware of the need to make compromises for the sake of the other person.
A part of his deal will be to do more around the house, definitely. He may need you to show him certain jobs though, and then for the both of you to sit down and come up with a written down list where the both of you establish who does what and when. Put it in writting so there can be no disputes later.
A part of your deal will be to be more tolerable for a mess. You have to understand, this is who he is and how he has lived his life. You can't realistically expect him to make sudden and dramatic changes in the space of a few weeks, or even months. So you too will have to comprimise.
Anyway, if he continues to slack, even after you've made a list together, then try not to get angry with him but instead voice your frustrations in a calm manner. Tell him how it makes you feel, with no distractions. Sit him down, seriously, and ask him to listen and not interrupt until you've said all you need to say.
We guys don't always understand exaclty how a woman is feeling, despite many hints or having said something a thousand times. We're just wired differently. And if you tell him in an aggressive/confrontational manner, he is going to put his guard up and not take in what you're saying and wanting.
If things still don't improve after this, and you can't stand it, make it obvious that you're willing to walk away from the relationship. And, if you have to, you have to.
If he can't compromise on this, that says a lot about how the two of you have different goals/values. And therefore, likely aren't an ideal match.
Hopefully, it won't come to that, but the best bargaining position is always being able to walk away, and mean it.
I hope that helps!