I would like to bring a small potted plant from Taiwan to the US as a gift for someone. Will US customs allow me to do this at all? I hear that there are some species of plants that are definitely prohibited. If plants are allowed, what are some good ones to choose or avoid to avoid problems with customs?
The best and simplest one would be not to travel with one unless it has a sentimental value since most potted plants you can get in the US and those you can't are probably restricted and you will be forbidden from importing it.
Having said that.
There is an entire section in APHIS from US Department of Agriculture dedicated to what can and cannot be imported for planting and the list of Prohibited Items. On top of this you should also be concerned with possible import of insects that may be dormant in the plant or in the soil such as Asian Long Horn Beetle, which has caused a lot of problems with tree populations in the US and specifically in New York.
If you want to bring it in legally you'd need a permit. Most likely you'd need (in trying to obtain that permit) a phytosanitary certification, and they'd probably want you to bring it in bare root (no soil). They may also ask that the plant stay at one of the USDA facilities for a quarantine period.
It will be relatively difficult for you to do this.
A few years ago, I brought a couple of desert roses from Vietnam. I cleaned and trimmed the roots, as well as obtained permits for the specific plant I wanted to bring, which was desert roses. Later on, they said I am not allowed to bring plants older than one year.