When buying a new telescope for observing galaxies and nebulas under $3,500, consider whether you want to photograph objects or just observe, and if you prefer an electric drive or a manual setup. Storage space and transportation capabilities are also crucial, as larger telescopes can be cumbersome. Attending local astronomy club events or star parties can provide valuable hands-on experience with different telescope designs and setups. A Schmidt-Cassegrain telescope is recommended for its portability and ease of use, while an 11" Celestron on a GOTO mount offers convenience and quality under the budget. It's important to budget for additional accessories like quality oculars and a diagonal to enhance your viewing experience.