I think you're looking for what's called a home equity line of credit (HELOC). For an appraisal of 360-390k and a LTV of 90%, you will be able to tap anywhere from $11,000 to $38000 of equity. The bank will walk you through the appraisal process after they conditionally approve your loan. They would be the ones ordering the appraisal.
Thoughts on cashing out.... I think it depends on what you plan on doing with the equity if you cash out. If you can pay down debt that is a higher % than the HELOC interest rate or put it in some form of performing investment, its a good choice. If you plan on buying something you otherwise wouldn't have (i.e. tvs and cars) I would advise against it. But,you put a lot of work into the house so if you'd like to enjoy your equity now instead of later, that's totally cool too. But remember the money isn't free.
If you have PMI, you will want to talk to your bank about having them pull the appraisal to have that removed (if your numbers are correct).