Here are some of my tips!

Just as an aside, what would you recommend to someone who has never eaten sushi before? Not a fan of shrimps or prawns, never tried crab, have no problem with smoked salmon and other cooked fish.

The field is yours.

I'd recommending that person take a look at the textures they like. Sushi is a very textured experience.
Smoked salmon has made it into sushi.

Personally, I'm not a fan of oily fish, so I avoid some of the fishier things like mackerel. Here's some things I would suggest to someone to try it:
Nigiri - this is the piece of food on vinegared rice.
Maguro - it's tuna, fairly good beef tartare like texture.
Octopus - it's cooked, chewy, taste
Tamago - it's a lightly sweetened omelet
Inari - fried sweetened tofu pockets filled with rice
salmon - because 'murica
hokkigai - steamed surf clam, it's delicious and a good chewy texture
tai - it's red snapper, lighter textured, and generally dressed with a little citrus vinegar, it's delicious

Some things I avoid due to texture for new folks:
uni - sea urchin roe, scallop

Rolls -
kappa maki - seaweed + rice + cucumber
tekka maki - seaweed + rice + tuna
godzilla - or some variant name, it's a rollow that's dipped in tempura batter and fried
california roll - because why not?

most restaurant rolls seem to be a variant of a dressed up california roll, so go from there. I'd avoid eel of any type though, personal preference, but I don't find it very good, texturally or taste wise.

HAHAHAHAHA. Just read about it.

Generally, if I don't know the traditional japanese name for a piece of fish being used in sushi, I won't eat it. That also helps me avoid a fish I see cropping up everywhere.

Tilapia. Sweet, a fresh water, farmed, trash fish as sushi? Good thing freshwater fish don't carry parasites that are zoonotic.