We do a bit of a mix here too... started with the finger foods because he always wants to hold the spoon and it ends up in his mouth... usually the right end...
So with the finger foods I usually just give him a bit of whatever I'm having as long as it's cooked til soft where necessary. Loves cheese and also toast with philly cheese on it... but doesn't seem too fussed about butter. Banana he sort of sucks on and then throws it to the floor. Watermelon didn't pass the test at all yet, so we'll try again next time i buy some.
The gag factor is something you just work with... it means I don't give him finger food in the vicinity of my mil who rushes over when he has even a tiny cough at a regurg... it freaks her out and defending myself about parenting decisions is something I can't do easily with her, so I'll pick my battles. So far he just coughs and splutters a bit when he bites off too much especially if it's something he's having for the first time. Eventually whatever it is gets spat back out and lands under his chin.
As someone else said, it's great being able to give them something when you're out and they get restless - great not having to take along a spoon etc too!
