What are the tests or procedures that I should have at the beginning of my pregnancy?

Depends. If you are seen in the 1st trimester, an OB profile (cbc, syphilis, hep b blood type, hiv, rubella). Optional, cystic fibrosis, sickle cell, HSV titer, first trimester screen for risks of birth defects. These are the most common.
Pregnancy. Women are usually checked for rubella status, hepatitis b status, syphilis, gonorrhea, chlamydia and blood type. And in later pregnancy women are screened for diabetes and gbs.