I have heard it said that it's best to strike while your spouse is distracted. Maybe your spouse will be so focused on getting free so he can date (live out his fantasy) that he won't making the split of resources more difficult.
The house question is really hard. As your stbx is living elsewhere, and so focused on his new self and life, I'm guessing that you'll be the one who will be getting the house ready for sale. Apart from the pain of uprooting yourself from your home, the market really is such that finding another place for yourself to buy with what you recover from the marriage won't be easy. Plus your children, even if they aren't living at home any longer, will lose their childhood home. This is the kind of pain and disruption our spouses cause, and yet they focus on themselves.
Don't put the house on the market until you've figured out where you're going to live, and when you want to move in. (If you find a place to buy you can negotiate a bridge loan until your house sells.) A good realtor can help a lot with the anxiety of selling the house. You can get a market assessment from several and choose the one you are most comfortable with. I hope you'll check with your lawyer about whether you can assign a monetary value to any work you do to get the house ready for sale--whether clearing it out or overseeing repairs or staging--and account for it in the settlement of assets. I had to go through so much in the house, just to move out (I sold my half to my spouse), and it was a emotionally painful task to go through 35 years of married life--I uncovered, for example, a copy of our wedding invitation, announcement, and the vows we'd written.