The roth conversion is taxed as ordinary income - this will be your "first dollars" of income. Since you say you sold "long-term investments", I'll assume that means the gains qualify for the lower long-term capital gains tax rates.
The long term capital gains may be pushed into a higher tax rate depending on the amount you convert.
Conventional wisdom would be to convert up to the standard deduction at the very least, so long as the LTCG remains in the 0% bracket there as well. Of course, if you are getting ACA subsidies for your health insurance, that would go into the equation as well. So as with anything tax related, I suggest figuring your overall tax with several options so you can make a better decision.