Arguably one of the most well known and observed nebulae is the Orion Nebula in the constellation of Orion. Orion holds a prominent place in the night sky all winter, and the nebulae will be easy to find along Orion's belt with the Celestron 130GT telescopes, a DSLR with a relatively wide lens, or potentially even the naked eye.
The attached image is the first astrophotograph I ever personally took, with a 70-200mm f/4.0 lens under relatively dark skies (Bortle 3).
On the topic of well known deep space objects, a photograph of the Eagle Nebula is arguably the most famous image ever released by the Hubble Space telescope.
The photograph, a false-color image (more on that later) depicting the star forming region The Pillars of Creation shows the elements Oxygen, Sulphur, Hydrogen, and Nitrogen. Star forming regions are areas in which dense regions collapse to form stars. Many prominent nebulae represent star forming regions, including the Eagle Nebula, the Orion Nebula, and the Elephant Trunk Nebula.
Depicted in the image by Hubble is a relatively small region within the already semi-small Eagle Nebula, however during summers, when the object is visible, it should fit nicely into view using the 130GT and 25mm eyepiece. The narrower eyepiece will help focus on this region specifically, however expect detailed viewing of it to remain somewhat difficult.
(NASA, ESA, STScI/AURA, 2017)
Image captured by wikipedia user Hewholooks, CC BY-SA 3.0
In the night sky, the California Nebula is very large, however not all that bright. Due to existing almost entirely in the emission bands of Hα and Hβ, the California Nebula is only visible through a telescope with a Hα or Hβ filter (more on these later). While some claim to be able to see it under dark skies and holding a Hα to their naked eye, this is debatable and not widely supported. Alternatively, due to its size, it is possible to catch this nebula in a photograph using a (non-modified) DSLR with a relatively wide lens, as long as you are able to capture enough light.
The Veil Nebula is another large but dim object. A filamentary nebula comprised of Hydrogen, Oxygen, and Sulphur, and primarily visible in the Hα and Oii emission bands. Like the California Nebula, while too large to fit fully into the field of view of the widest (25mm) eyepiece, it is unlikely you'll be able to observe it with the small 130mm telescopes and no filtration. Even with a non-modified DSLR the object is remarkably elusive.
Image by Ken Crawford, imagingdeepsky.com
Incredibly large and bright, the North America and Pelican Nebulae are prominent all summer at the heart of (what we see as) the Milky Way. Through the school's 130mm telescopes, even the widest (25mm) eyepiece is too narrow to catch them fully in frame, however a (non-modified) DSLR with a relatively wide lens should be able to capture them easily, and under dark skies they should be visible to the naked eye.
Nebulae present a set of challenges completely opposite many of the other objects one can observe. While many are very large in the night sky, they often have a low surface brightness that renders them invisible to the naked eye (or even a small telescope). To observe nebulae, often the wider 25mm eyepiece is required to avoid filling the frame with too-narrow a view.
The other important thing to keep in mind is emission bands of the nebula you wish to observe. Nebula who's light is primarily concentrated in bands that humans struggle to see (such as the Veil Nebula) will be significantly more difficult to observe, even if they have a similar surface brightness to an easier-to-see object.
Nebulae are often best photographed with a modified DSLR, which has had its low- and high-pass filters removed, so important bands of light are not blocked before reaching the sensor.
While use of a modified DSLR (or purpose-build CCD or CMOS astronomy camera) allows important wavelengths of light to reach the sensor and capture images, the best detail, and great significance of data is achieved when narrowband filters (which let light within a only certain set of wavelengths to pass) are used to focus on a certain emission band.
A detailed explanation of how this narrowband photography works, and why it is important, is written in the presentation linked below.
Due to their incredibly diverse compositions and structures, the greatest educational significance that can be derived from observing nebulae comes from understanding the gasses of which they are comprised through spectroscopy. Spectroscopy is the process of breaking down light into its component wavelengths. In astronomy, this is used to gain a better understanding of the gaseous composition of stars, nebulae, galaxies, and many other objects in space.
Intro to Spectroscopy and Where it Gets Complicated: Richmond, How do we know the composition of stars? http://spiff.rit.edu/richmond/asras/chemcomp_i/chemcomp_i.html
Veil Nebula Image: http://www.imagingdeepsky.com/Nebulae/NGC6960/FullSizeJpg/NGC6960.jpg, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=30574320
California Nebula Image: Hewholooks, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4261893
NASA Messier Catalog: https://www.nasa.gov/content/goddard/hubble-s-messier-catalog