Since you are driving an inductive load, over current and Short Circuit protection are going to be a little tricky.
You could try a Triac module that has this built-in. Not always the cheapest solution, and one that may come back to haunt you if the design is long term and you need to maintain it 5 years from now, if the device is obsoleted. Fast blow fuses inline can help, but are a nuisance if they can't handle the inrush, or the Triac dies before the fuse.
For absolute SC protection you are going to need intelligent current sensing. You will have to monitor load current, decide what is beyond inrush, or is a sustained short, and disable the power source. This can get messy and complicated, and probably beyond what you need to do.
I would choose a Triac that is capable of handling the available supply, with generous headroom, then protect it with a snubber. Honestly, I have seen more Triacs die an unatural death from exceeding their dV/dT rating, than from a SC's that were not designed out in the first place.
I would also change to a zero-crossing opto-coupler, unless for some reason you absolutely have to have random phase triggering. You said you are controlling solenoids.. can they wait until a zero-cross to be operated? At 50Hz, given a solenoids electrical and mechanical behaviour, I think zerocross switching should be fine.