If you're starting from zero, try a $1,000 starter goal. It may be easier to stay motivated if your target feels manageable and within reach. And $1,000 is still a nice chunk of change that could help you weather an expensive car repair, emergency room copay, and more.
Once you reach your initial goal, keep going! Many personal finance experts recommend keeping six months' worth of living expenses in an emergency fund. This gives you a nice cushion in case you lose your job or need to take an unpaid leave for other reasons. Certainly, the current Coronavirus pandemic has taught all of us the importance of preparing for months with a reduced income or no income.
Ultimately, you know your situation the best. If you work in a field with more job security, such as education or healthcare, you may not need six months of income. On the other hand, someone who is self-employed and supporting a family may want to have a whole year's worth of income saved.
Action Step: Set an initial and an ultimate goal that works for your life and budget.