I wouldn't pay for an appraisal before you apply for a loan. When you refinance, the bank arranges the appraisal as part of the loan process; I'm pretty sure that most banks won't accept an independent appraisal.
You can make your own estimate of your home's value by looking at recent sales of comparable homes. A pretty good place to start is Zillow. This isn't as good as getting an appraiser to look at your home, but at least it won't cost you anything.
We are trying to refinance right now, so I think it is a good enough time to do it. Rates are low right now. Rates may be lower next year... but on the other hand, we might not be able to refinance next year because my DH might get laid off again, or our property value may go down further. So we want to take advantage of the opportunity now, if we can. If rates drop a lot more next year we can try to refinance again.