Most of them seem to like cilantro.
Vietnamese coriander - a type of cilantro - can be grown indoors.
Basil is doable, but supposedly challenging.
I sent a friend a topiary rosemary once. Like one of those tiny japanese trees, only rosemary. She thought it was cool, but she mostly used it to make chicken - which may not be vegetarian enough for your sister.
As for frozen veggies… when you're not buying meat, it is much easier to afford luxury organic purple bell peppers off season.
As for spices… I usually get high quality, low price spices at the ethnic grocery stores. Like the one run by chinese people, with 90% of the item signs written in both english and chinese. If it doesn't smell a little funny when you walk past the giant stacks of 50 lb bags of rice when you walk in, you're in the wrong place.