I just finished building by ss. It's not a fixie but I got heaps of experience.

Frame is the most important. Choose your frame wisely, it needs to have horizontal dropouts instead of vertical. It's doable with vertical dropouts but it's going to cost you more.
Tyre clearance: What sort of commute you do every day? What tyre size will fit into the frame?
What is your goal when building a fixie? What is your commute route as you will need to choose the right gear ratio for your bike
Chain: Do you consider using standard chain or half-link chain?
Budget: How much do you want to spend on the project, what parts and tools you have available?