Praise be to Allah.
The Internet is a means that may be used for good or evil, what is permissible and what is prohibited. If those who use it are not religiously committed people who adhere to the limits set by their Lord, then their usage may not be free from haram activities such as downloading images, music and movies, and participating in immoral chats, and the like. Therefore it is not permissible to give an Internet connection to anyone who you think most likely will use it for haram purposes. You should choose those of your neighbours who you think will never use it for haram purposes. Otherwise, you should keep your connection to yourself, even if it costs you more, so as to avoid helping anyone in sin.
You can also get a connection from an existing group that is already sharing the Internet connection, then you will be free of the issue of helping others in what is haram and telling them about it.
And Allah knows best.