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Both good ideas but you usually won't know before you go if there are kids in your family so it's difficult to tailor the gifts. I've pasted my response to similar questions below. Happy trails!
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For host family gifts I like to take/send items that represent our area. In addition to a food specialty if there is one (maple candies, chocolate covered cherries, etc.) things like photo magnets, playing cards, tiny photo books, and picture calendars (even if it's most of the way through the year) with a state or regional theme make good gifts. I can see Mt. Adams in Washington state, Mt. Hood in Oregon, and the Columbia River from my house; I have photo magnets made and they're a big hit in the tropics because no one can believe I see snow year round. When I find a good deal on small English/Spanish dictionaries I take those to give out to teachers and family members and (in my case now) scholarship students. You don't want to take anything too fancy or it might make them feel uncomfortable or like they should reciprocate.

For kids I take small rubber finger puppets, stickers, pencils, and small pencil sharpeners; I don't give out candy or balloons for health/safety reasons. Sometimes I find those glow stick/bracelet things at the Dollar Store and take those, and some little hair doodads for girls. Pro team apparel/hats are popular but spendy and a lot to lug along if you don't know anything in advance about the family.

I don't give money to kids who ask (beg) for it but foreign currency can make a fun gift for host family kids if they're old enough to keep it out of their mouths - all the coins and a $1 bill, maybe.

Taking your family out for dinner or dessert is a fun gift idea and your teacher would appreciate that, too. Sometimes you'll notice something they don't have you think they'd like that you can buy locally. A few times I've taken a nice portrait of the family for my own memory keeping but have framed an enlargement as a gift before I left.

One of my best recommendations is to take a small photo album of your own family, house, pets, town, and friends - the perfect conversation starter, esp. if there's a language barrier. Happy trails!

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If I bring anything from another country, it has to be small, light and non-perishable (pens are a good idea) and people seem to like things with a country's logo/symbol -- Canada's red maple leaf, Australian flag/animals.

However, being pragmatic, my first choice would be a gift basket of various food items that can be bought locally.