Would taking a mood stabilizer instead of taking anti depressants and anxiety medication be a better option?

If Bipolar, yes: People with bipolar disorder risk switching into mania when given antidepressants unprotected by mood stabilizers. You would need a full evaluation of your condition to know -- you can see a psychiatrist for this. Only after this thorough assessment would a psychiatrist be able to answer your question properly.

Not enough info: A better option for what? It is not clear what symptoms you are experiencing or what conditions(s) you are trying to treat. Unless you have a bipolar mood disorder, a mood stabilizer would not be indicated. If you are dealing with common anxiety and depression and meds are not helping, your best option is psychotherapy, not another drug. Medication alone is not optimal treatment.