You're making some smart choices, congrats!
I've come from a similar spot. Had a mess of collections, student loans, etc etc. Took a long time to get my head above water,
With interest rates being so low and home values so high, a refinance is not a bad idea right now, but make sure you have a trusted mortgage broker who will give you the details all up front. I recently refinanced, and it was a no brainer, home went up in value so I got rid of PMI (mortgage insurance) because my owe to value ratio came in under 80%, got a better interest rate, went from 4.25 to 3.25. And I threw in a couple credit cards. So my mortgage payment went down $300 a month and I got rid of the last of my credit card debt that I was paying $300 a month on. $600 a month in the black on the deal made it a no brainer. And I still have like $90K of equity in my home based on its current value.
When you get out of debt, the most important thing is to build a good emergency fund so the next emergency you won't go right back into debt. Credit Card debt just makes you feel hopeless, it never goes down and one bad month can get it way back up there so you get stuck paying indefinitely. If you're left with some CC debt still, once your credit gets better, your CC companies will send you 0% balance transfer options. Transfer debt to that card and pay 0% interest on it for a period, when that runs out look for another 0% transfer offer. My wife has some cards that she transferred to 1 and is paying 0% interest for 36 months, she's on track to pay it all off well before 36 months expire.