Mortgage Refinance Question/Advice/Thoughts

So I need to refinance my mortgage... not just cause rates are good... I have a short-term loan on the house, needs to be refinanced.

So I started calling around yesterday since rates popped down.

I am only about 40% levered on the house, so have an option to take cash out.

Some options I'm considering:
- Refi vs. Cash-Out Refi: I am considering just refinancing the current balance, or cashing out up to the conforming loan limit... would net me a decent chunk or so in cash. At the moment, I'm getting rate quotes that are the same either way

- 30 year vs. 15 year. Best quote I have today is 3.625% on the 30 year, with about $1k in closing costs (which I could roll into the note). Best quote on a 15 year is 2.875% with about $1,600 in closing costs (again roll in).

Intuitively it doesn't make a ton of sense for me to be so underlevered, so I might as well take cash out at such good rates. I can put it somewhere... a little nervous about the market for the next 6 months or so, but I various public/private investments I could make. Alternatively, paying less every month feels good!

Same issue on the 30 year vs. 15. My gut says go 30, if I want to pay off quicker I can, and the cost of having the option to pay off slower being that 0.75% extra on rate isn't that bad when rates are so low anyway. Plus I have the extra cash every month to invest...Alternatively, I could do the 15 year, and would feel better in 5, 10, 15 years when I've paid off a lot more of the debt.

So I'm leaning 30 year with the cash-out.

Any opinions?