What would a professional use to switch sprinkler solenoids?

Several comments:

• If you don't need isolation, then (obviously) you don't need any device that includes isolation, such as a SSR. If you do need isolation, you probably don't need it for each channel. A single isolation gap, for all 16 channels, should be enough. All this could save you money.
• Snubbers don't protect the switches (the SSRs, in your case). They just reduce the probability of false triggering. False triggering is not a harm for your switches (they are there to be triggered, even continuosly). The false firings are an inconvenience (or an obstacle), if your application is such that the load should never be powered when you don't want it to (e.g., you have an electric saw, there's been an accident, and you need to switch it off right away).
• Since the 24 V are AC, if you use unidirectional switches (such as MOSFETs, or BJTs), you will need two switches per channel.

EDIT: a MOSFET is unidirectional, because it conducts in both directions, but it blocks in only one direction. For instance, a normal silicon NMOSFET cannot block current from S to D, due to the parasitic diode it has. Since that diode is there, if you want to use MOSFETs for AC, you CAN, but you need to put two in anti-series (with their sources tied together, and their gates tied together), or otherwise you won't be able to block in one of the two directions. GaAs MOSFETs don't have that parasitic diode, so one device would be enough, for AC.

• I would go for a cheap TRIAC per channel (probably, without any snubber, because 24 VAC is such a low voltage, that you probably won't hit any dV/dt limit).
• A cheap TRIAC like this one would work.