>Should I use all GFCI and risk a "nuisance trip"
I would if they said that their equipment didn't cause nuisance tripping.

But if you can't test in advance and they won't waive you on it, then there is a real risk that they have dirty equipment.

>I've been told not to mix surge protectors and GFCI's on account of shunting of spikes tripping the GFCI.
That is true with some brands.