Questions about surge protecting ungrounded outlets

I'm having a hard time finding clear answers to my question so I thought I'd start here. I just bought a house that was built in the 1950's but an addition was added in the early 2000's. The electrical panel is grounded and all of the outlets in the addition. Are grounded 3 prong outlets. However, the rest of the outlets in the house are ungrounded 2-pronged outlets OR ungrounded 2-pronged outlets.

I want to set up my work from home computer with extra monitors as well as some music recording equipment in the basement, but all of the outlets are ungrounded 3-prong outlets. Safety is most important, so what can I do with these outlets to ensure everyone's safety first? Is a GFCI outlet at the beginning of the circuit the right move? Then, what can I do to protect my equipment? Since the panel is grounded, will adding a surge protector to the panel help even on the ungrounded outlets?

I know surge protecting power strips work by rerouting the current through the ground, so that wouldn't help with surge protection since the outlets are ungrounded. But is it inherently more dangerous to plug a 3-pronged power strip into an ungrounded 3-pronged outlet?