The answer to the question of whether you should take your clothes off for a massage is simple: it's totally up to you. The point is that any removal of clothing should always be optional. You define your comfort, not your masseuse. It is quite common practice to undress until you are in your underwear to receive a massage, as the rooms are usually quite warm and this allows the masseuse to work comfortably and effectively across your back, arms and legs.
If you give your consent, massaging the glutes (gluteal muscles) could help relieve lower back pain. A blouse with thin straps is a great option as it will allow you to cover yourself, but still make it easier for the masseuse to work on your neck and shoulders. For chair massage, people usually stay fully clothed and simply take off an outer layer, such as a sweater over the top. For table massage, anything you want to wear is fine.
The most important thing is that you're relaxed, which you can't be if you're thinking about clothes. It's good to know that many massage therapists are trained to allow you to choose the amount of clothing you'll take off. Most commonly, clients remove clothing that prevents skin-to-skin contact in the areas to be treated during the massage treatment. If you want to keep your clothes on, you can wear something that is comfortable and allows you a little movement.
If you're wearing underwear, the masseuse will gently place a sheet around your waist to protect your clothes from massage oil. Chair massage (oil-free clothing) is an excellent introduction to massage, as is doing a neck and shoulder massage (with clothes on). The general rule is that the customer defines their own comfort zone based on the amount of clothes they lose. Thanks for reading and I hope this is useful.