For example, I will not be contributing enough to max out my HSA contributions, so would there be any benefit to putting extra money for my child's braces into the LPFSA, or should I just put it all in the HSA?
If you know you will have a big bill, like braces. and you fully expect to hit the deductible then it can make sense. The deductible can trip some people up, because if they put too much into the limited purpose FSA and don't hit the deductible for the regular insurance policy, they can't get to all the money in the FSA.
Because you have the ability to spend the potential money in the FSA before all the money has been contributed, it can allow you to make that payment for the braces in January. I did this the first year we had the HSA. I knew I needed to pay a dental bill early in the year. But the HSA would only have a few hundred dollars at that time, so I used the limited purpose FSA to be able to make that payment. This could also work if you spent a lot of money in the previous year.
Because you have the ability to adjust how much money goes into the HSA each each pay period, this idea does keep the option open to fully fund the HSA if your finances improve.
Regarding the deductible.
The law limits what you can use the limited purpose FSA for: dental and vision only. There is an exception. If you hit the deductible for the high deductible insurance policy, then you can use the funds in the limited purpose FSA for ANY medical reason.
When I did this a few years ago, I needed to send extensive paperwork to the company holding the funds before they would release the funds for dental. Once I sent them proof that I had met the deductible, then any medical expense after that date could use the FSA with minimal paperwork.
If you fully fund the FSA beyond the cost of the braces, and then have a light year medical expense wise, you might not be able to spend all money in the FSA by the deadline.
Regarding state taxes. I saw no difference in my states (Virginia) treatment of the funds. The state taxable income number was exactly the same as the federal taxable income number. It did not treat the money in the FSA differently than the money in the HSA.