Don't be intimidated about conducting archival research, especially if it is your first time. Every scholar, historian, and academic had to start somewhere. Each time you visit an archives, you will be adding more experience to your research knowledge and gain more confidence. This will be a great asset to you throughout your career, whether it's in academia or in industry.
Some archives will make you wear white cotton gloves. Some don't. It depends on local practices and on the types of materials you are handling.
At the New School Archives, we won't generally ask you to wear gloves, but there are always exceptions. We try to protect our materials in ways that allow you to handle them without directly touching sensitive surfaces. The collections are here for your use. We're here for you to do research.