It depends on what kind of job you want and what your financial state looks like. Some jobs will only take an LMSW (e.g. some medical social work positions, some jobs associated with the state/federal government, etc.) while others do not care. If you want to get licensed as an LCSW, you will need to be an LMSW, so you may want to prioritize that.
Your best option though, is to do both at the same time. Seeking employment is going to take a while, so you can study for the exam while you do so. You can study and take the exam while you are working after you get the job as well. However, if you have the financial flexibility to not work for a little bit, then use that time to cram for the test and take it. It does not take very long to study for the exam, so you could feasibly do it in as little as 1 week to 1 month.
You don't necessarily have to pick one or the other. I would definitely recommend putting your resume out and getting familiar with the labor market in your area, that experience itself will be valuable whether you decide to accept a position or not. Most of us need to practice our interviewing skills and the entire process of applying for employment also needs constant refining.
There are usually study groups you can join to help prepare for the licensure exam, either formal classes where you pay or informal classes that someone just starts. If you can find out in your area, those may be helpful too.