I disagree with the other answers. I believe your best choice is a simple "cash out refinance" instead of a home equity loan. The reason is your interest rate will likely be lower with a "refi" than a home equity loan. For example, the difference between 4% and 5% would end up saving you almost $6K in interest on a $100K loan for 10 years.
The biggest downside of the refi is you have to pay much higher closing costs (could be more than $1K) than you would with the home equity loan (which sometimes have no fees at all). If you were only borrowing the money for a year or two, the extra fees may not be worth it, but you stated you're thinking about a 10-15 year term. In that case the lower interest rate should easily make up the difference compared to the fees.
Obviously this all hinges on the fact that a cash out refi rate will be different enough compared to the home equity loan rate. Shop around and make sure this is true for your situation.
Side Notes:
- The above assumes your home equity is quite a bit more than $100K.
- What you want to do really ought to be called a "cash out finance" instead of a "cash out refinance", but alas, no one calls it that.
- Beating a dead horse here, but, with few exceptions, someone who amassed $100K in credit card debt is unlikely to pay you back in full in your lifetime. I got the impression you know this and are OK with it, and that's really nice of you.