Much depends on how dark the skies are that you will be observing from. A 6" refractor should be able to show quite a few galaxies, somewhat fewer than an 8" SCT, but still quite a lot. Brighter skies will steal galaxies more rapidly than loss of aperture, because the surface brightness of most galaxies is not that high. To give an idea of how little aperture is needed: with only 42mm of aperture in very dark sky I was able to view that ~12 mag supernova in NGC 4636 the other night, and see the 9.5 mag galaxy as well. They were downright easy with the 60mm scope when I estimated the SN at 12.4 mag.
Assuming rural dark sky, anything on the Messier list will be well within reach as well as the Herschel 400. The dimmest on the Hershel 400 list are about 13 mag photographic (and 0.5 to 1 mag brighter visually.)
Perhaps one of the best ways to improve your skills is to pick a showpiece galaxy and try to sketch what you see. The more you study it, the more you will see. Another way, is to use a more detailed image of the galaxy and see what you can identify visually, checking off knots, arms, bars, stars, etc. In some ways this can be more helpful than sketching because it provides a rapid feedback loop for suspected things, and can indicate where to look for others that you might otherwise not notice (because it is easy to tunnel in on more prominent things even when sketching.) Combining the two captures the benefits of both.
Along with showpiece galaxies, pick a few you expect to be challenging and see what you can detect. Clusters or strings of galaxies can be quite rewarding as you will have a range of brightness/shape objects to try to detect. It helps to bring a more detailed chart to the field so that you can identify and check off what you see vs. what you don't. The smaller the apparent size, the more magnification that is often required to see a galaxy.
If you don't sketch, just try composing some notes in your head for what you do see, even if you don't record them in any fashion. For example describe the general size, overall brightness/dimness, surface brightness (e.g. high, average, low, very low), general shape/orientation, any lumps/knots other irregularity, whether the galaxy brightens to the center noticeably, or has a stellar core. If you see an orientation describe the general alignment, e.g. NW/SE elongated 2:1. Sometimes you might see a brighter bar that is prominent, but realize a very low surface brightness wider expanse/elongation of the galaxy is turned nearly perpendicular to it. Describe any nearby stars/asterisms.
The above paragraph might sound like busy-work, but having some key things to record prompts me to spend time studying each galaxy before moving on to the next.