One of the most confusing things in the field of psychology for a lot of students is figuring out not only which sub-field to specialize in (e.g., counseling, clinical, I/O, etc.) but also what level of education to pursue - so you are not alone in having this question! So you know a little about my background, I have a PhD in Counseling Psychology.
First, you will need to consider what type of work you hope to pursue once you are finished with your education. If you hope to provide direct services, generally a master's degree is all that you would need. Master's programs in Counseling/Clinical are generally designed to prepare students to be practitioners and help students become Licensed Professional Counselors (LPCs). If you hope to also engage in research or teaching at the college level, then a doctoral degree is generally required. Doctoral programs, in particular PhD programs, train students to be both scientists and practitioners, and programs will vary in the degree of emphasis they place on those two areas of training. This is why most doctoral programs will want to see that you have research experience before applying. A doctoral degree can also allow therapists to have more autonomy in their practice. However, states will vary in their laws for the practice of master's-level and doctoral-level practitioners, so it will be important to gather information about the practice of psychology in whichever state you hope to live.
Second, some of this will depend on what you consider to be a "stable job." The Bureau of Labor Statistics Occupational Outlook Handbook (www.bls.gov/ooh) can provide you with a ton of information including average salary and job outlook for mental health counselors and psychologists. The good news is that there is a need for both levels of professionals. What can be helpful to do beyond looking at information online is to reach out to an LPC and a Psychologist in your area to talk with them about what their day-to-day life is like as professionals, what they wish they had known, and other questions you have about these occupational options - these are often called informational interviews.
Finally, there are a ton of other factors to consider including things like the length of time you want to spend in school, funding opportunities in different programs, application requirements for programs, etc. It can be useful to start to look at both master's and doctoral graduate program websites to get a feel for some of this.
It can be overwhelming, so know that you will never have all of the information and will have to eventually make the best decision for yourself with the information you have while remaining open to opportunities as they come your way. If you are currently a student at a university (or are an alum of a university), know that your school's career center can be useful for guidance as well - if you haven't reached out to them yet (or to a professor in your Psychology department), that would be a great first step for getting support as you make this decision.