I hear ya on the throw up. Yuck. I always offer the 'real food' and then put a few cheerios on their tray so that something is a least familiar and easy for them. Most of the time it doesn't take very long before they are on to some more options.

Here are some of my go-tos:

grated apple
avocado
cut up grape tomatoes, cucumber, peppers (I cut them up really tiny)
cottage cheese
hummus
muffins, banana or zucchini bread
cheesy bread sticks (made from dough in bread machine.... yum!)
cheese cubes
apple sauce
oatmeal
toast fingers