General Thoughts
In general, if you have pets or children prone to eating random things, don't get house plants or put them in a place that it is impossible to get to. Plants that adults can handle may be bad for tiny humans.
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The easiest plants to grow are going to be:

Hoya - These are fun. Generally, not poisonous. Pretty easy to care for and have neat, nice smelling flowers.
How to Grow and Care for Hoya Plants
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Peperomia - Not poisonous. Also, lots of varieties and easy to grow.
How to Grow and Care for Peperomia Plants
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Peace Lily - I put this here because if you want to send a plant for bereavement, this is a common one. My team sent me one when my father passed. Mine is blooming again. Toxic to pets and people.
How to Grow and Care for Peace Lily Plants
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Philodendron - Lots of varieties as well and easy to grow. I've had one since the 4th grade. Poisonous to pets and people.
Philodendron Varieties: How to Grow Indoors
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Pothos - Fast growing and easy. Toxic to pets and people. Lots of varieties.
Pothos: Plant Care & Growing Guide
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Snake plant - These are very common and are one of the best for removing toxins from the air. Very easy to care for and lots of varieties. These are mildly toxic, but mostly safe.
Snake Plant: Benefits, Types, Cautions, and How to Grow
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Zygocactus - Generally, not poisonous. I've had one for years. I added it here because I think people enjoy flowering plants, especially those that bloom around holiday season. You can get them to bloom again, but I believe it blooming is light dependent.
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ZZ plant - I've always wanted one of these, but I didn't get one because I had to keep some plants away from my cat. These grow virtually in the dark. I personally think they are super cool. Toxic to pets and people.
ZZ Plant (Zanzibar Gem) Growing & Care Tips
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Other Favorites

Orchids make great gifts. From what I understand, only some are poisonous. There are a lot of options and the blooms last forever. You need to make a little bit of an effort to get them to bloom again. Fortunately, recent breeding efforts has made getting them to bloom a little easier. I have 5, and I have successfully rebloomed 2.
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Bromeliads are pretty cool. Non-toxic to people and pets. These are the same family as pineapple and have striking blooms that last a long time. I got 3 last year.
How to Grow and Care for Bromeliad Plants Indoors
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Money tree - non-toxic to pets and people. Considered good in feng shui.
How to Grow and Care for the Money Tree
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Thoughts about other plants-

Ficus are mostly difficult to grow although I've had a long suffering one for many years. They do not like changes in environment so would be a risky plant to ship.
Monstera can be a huge plant. Kind of like philodendrons on steroids. Palms are generally temperamental as are ferns.
Dieffenbachia - is also known as dumb cane. If you eat it, your vocal cords can be paralyzed.
English Ivy - Why? Those things are weeds.
Begonia maculata - I have had one for years, but I have less than ideal conditions. I regularly take cuttings and start anew.
Calathea/Maranta - (prayer plants) are cool, but they need more moisture.
Spider plants were all the thing when we were kids because people did the whole hanging plant thing. I think these are coming back into fashion although I find them boring. They are generally non-toxic. These guys are also good air purifiers, and there are more varieties than there used to be. So not a bad plant.

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