Medications work differently for different people. I know someone who has taken Enbrel for a decade with very few problems, but it gave me intolerable side effects and I had to switch to Humira. Finding the medication that works best for you is often a trial and error process and may take a while. On the other hand, it's quite possible that you'll react brilliantly to the first medication you're prescribed - it's impossible to say. As well, some people react very well to a small dose of a medication, whereas others need a larger dose.
Advil only provides symptomatic relief of pain and swelling, but does not address the underlying cause. RA is usually treated with DMARDs (disease modifying antirheumatic drugs) like methotrexate, Paquenil, the Biologics, etc. Often, these types of medications are accompanied by prednisone as a sort of "booster", although prednisone alone can also slow joint damage - I suspect that's why your doctor prescribed it. I don't know why your doctor didn't prescribe a DMARD with a low dose of prednisone, but that's something you can discuss in your next appointment. I would recommend that in future, if you are concerned about the medication you're on and/or its side effects, you discuss your concerns with your doctor instead of stopping the medication on your own. You and your doctor are a team and need to work together to treat your RA. You're the person in charge of the team, but treat the doctors, nurse practitioners, physiotherapists, etc. that you'll meet in your life with RA as the expert consultants that they are. Asking questions, doing research and educating yourself about the disease and the treatments is very important and your doctor is one of the resources available to you.
Most of the time, side effects of DMARDs will be manageable, rarely, if ever, preventing you from going to work and living your life. These drugs are meant to help you live your life by suppressing the disease to minimize pain and joint damage that will otherwise affect your ability to live your life. Last year, I wrote a post about how to manage side effects and you can read that here. And remember that your doctor is there to help you, so ask all the questions you need to feel comfortable and safe.