Some SSRs will use a TRIAC as their switch element. The thing about them is they continue to allow current to flow until it reaches near zero, when they switch off. This is no problem for AC where the current goes to zero 50 or 60 times a second, but doesn't work for DC. Those use MOSFETs or some other switching elements.
Also, there are a complex matrix of overpriced industrial SSRs, expensive but very good industrial SSRs, inexpensive but good industrial SSRs, cheap but not good industrial SSRs and knockoff SSRs of each of these. If you're a mass manufacturer you don't use any of these but rather implement the SSR design yourself.
Also worth knowing is that the common failure mode of an SSR is to always power on. Make sure that is OK with your use.
I think practically anything will work with what you're planning to control so far, but provide a link to which SSR your thinking of using and for what exact purpose for specific advice.