Because almost all of your electrical equipment has microprocessors in them or some form of electronics I have recommended a whole house surge arrestor for a number of years now. Just think of the damage a spike (lighting strike) can do to any appliance plugged into your system. Sure you have insurance but think of that pesky deductible and then there is the argument for actual cash value (depreciation) and then the hassle of getting everything replaced. In other words it's worth it.
Now on to your question. The NEC provides an entire section on these devices now Article 285 (by the way yours is an SPD Type 2. Also it is not raintite so if mounted outside it needs to be in a raintite enclosure N-3R. Article 285.12 tells us we must keep the conductor length as short as possible and avoid any unnecessary bends. Article 285 will also refer you back to Article 230.82 (8) and 230.90 which will tell you that the conductors to this surge protector must be protected with overcurrent protection either in the form of a breaker or inline fuses is you elect to install this at the main breaker or any breaker larger than the required protection.
FYI You can only "double lug" conductors if the lug is rated to receive more than one conductor. Bye the way your doesn't allow it. I also took the liberty to look up the proper breaker size for your SPD.CHSPT2 family of products require a dedicated 2-pole 50 Amp thermal magnetic breaker.
FYI-2 Your panel has major problems. First there are what looks to be 2 #12 or #10 wires tied onto your main lugs in the panel these are undersized and unfused and dangerous, also see double lugged FYI. Second your Panel space is used up. You might go with @Harpers suggestion or consider installing a subpanel right next to it to get some more breaker space.
Finally I would like to say that even if you install the SPD in the panel it is installed to the bus and the only thing it is not protection is the service feeder from the main breaker. So it would be a safe bet it would protect all of the circuits downstream.
Hope this helps and good luck