Just like the considerations taken when choosing livestock; similar ones should be made when deciding what type of dairy animal to choose. to get a feel for them; let me walk you through my decision-making process.
What dairy products do we want? In this house we LOVE dairy. To drink, yogurt, cheese, butter, creme for coffee, ice cream, whipped cream, cream cheese the list goes on. Knowing what dairy products you want, will help zone in your research. For us, we wanted animals and breeds with high butterfat (cream) content and high-volume production.

What is our property like? The acreage and landscape you are working with will also play a role in your decision, unless you plan to bring in feed year-round. We live on two acres, half of which is wooded. With this in mind we decided we need animal that is a natural browser so they could feed off the property during the warm season.
Housing: what size barn do you have, or can you provide? We built a small 8×16 foot barn to house chickens. Not much space, so the barn says we need a small-medium animal.

Experience: what is your experience with dairy animals? As a complete noob, I knew I wanted a smaller animal that I could physically man handle if needed. Within the realm of experience was my concern of having to assist with a birth. The availability of Vet help is damn near nonexistent so being well known for unassisted births was a must.
Children: do you have children that will be around the animals? We have four small children who all love to help when and where they can. I know there is no way to completely prevent injuries, but I can mitigate them. Smaller animals tend to mean a smaller potential for injuries.
Taking stock of all these topics, we settled on a small breed and our research brought us to either, a Highland cow or Nigerian Dwarf goat. Although the Highland is small where cows are concerned, they are still too big for our current infrastructure. Nigerian Dwarf it was!
They are a stocky little breed that is well known for our main considerations of unassisted births, high butterfat, and volume. These are just a few basic considerations, hopefully it gets your wheels turning for your own preparation. Happy milking!