Following I want to give a short overview about the topic "Visual Observation of Deep Sky Objects". A bit more detailed is the paper Einführung in die visuelle Deep-Sky Beobachtung ("Introduction in Visual Observation of Deep Sky Objects") of Thomas Jäger, Wolfgang Steinicke & Hans-Jürgen Wulfrath, which is only available in German!
How wants to make notes of the observed objects, might find this blank protocol (only in German!) as template useful.
Deep Sky Objects are in general all objects located outside of our solar system. Basically we distinguish between galactic and extragalactic objects, so objects within & outside of our Galaxy. Following object types are visually of special interest:Galactic Objects:
Partially there are also objects within other galaxies observable. These are mainly emission nebulas (e.g. NGC 604 in Messier 33), large star associations (e.g. NGC 206 in Messier 31) or bright globular clusters (Mayall II in Messier 31).
Besides the mentioned types there are sometimes Novae or Supernovae visible, which mostly appear as stellar objects. Supernovae are not seldom present in distant galaxies.
Observing the sky visually might be one of the oldest tasks in astronomy. While formerly observations were fundamental (the New General Catalogue, in short NGC, is based solely on visual observations), these are today more a personal journey of discovery. Experiencing the miracles of the cosmos is appealing for most of us. Some do this in a more relaxed way, others (like me) prefer it more sportingly. But in the end, everyone can choose its own way to have fun and get diverted from the daily routine. Besides the pure visual observation a documentation of the seen is for many observers an important part. Short notes, detailed reports or object descriptions, but also sketches are common, which can show impressively the personal development over the years.
Not necessarily, because there a some objects already observable with the naked eye. Under halfway dark skies objects like Messier 31 (Galaxy, And) or Messier 44 (Open Cluster, Cnc) are obvious. The open cluster Messier 45 (Tau) is visible even from the city without any equipment.
With binoculars there are a lot of objects reachable, so that you can be busy whole nights. A dark sky is of course highly preferable, however even under suburban skies many objects, including some brighter galaxies from the Messier catalogue, are feasible. Therefore I can highly recommend to make some attempts with binoculars. Even I was really surprised, what an 8x40 binoculars can show under NELM 5.0 mag skies.
For fainter objects or details telescopes with an appropriate aperture are a must. Which aperture you choose in the end, depends from several factors, which will be not discussed at this point.
A very good question, which is hard to answer. From my own experience I can say, that perception can differ extremely. I have met laypeople, who can easily see the dust lane in the galaxy NGC 891 with 8 inch for sure, others had basically problems to see this galaxy at all. At this point I want to keep this topic short and would recommend everyone to meet amateurs in the immediate vicinity to get a tentative possibility for discovering the sky. Basically the sky offers a lot of objects, which can be discovered and can reveal details depending on aperture.