Yes, it is possible to choose a sperm donor online from a sperm bank's donor book/catalogue and have it shipped home for DIY artificial insemination or at-home artificial insemination. Firstly, you choose the best donor for you by just carrying out a search. Most sperm banks allow you to limit the search according to your needs and the type of donor profile you wish to look for.
Suggested for you: How to Find a Sperm Donor? – Tips for Choosing the Right One.