Whether you'll be able to see them depends on the levels of light pollution in your area. As TildalWave mentioned, a number nebulae and galaxies are perfectly observable with the naked eye so unless you live somewhere very bright, you should be fine. Under really dark skies, objects like M31 are very easy to find with the naked eye. Where I live, I hardly see it with a bright binocular due to very poor seeing, induced by a large number of shopping centres fond of pointing powerful searchlights at the sky for whatever reason.
As to how much you'll be able to see, you can get a general idea of what you should be able to see in ideal conditions by calculating your telescope's limiting magnitude
In reality, you'll also have to factor in the quality of the optics (mainly transmission), both the telescope and the eyepieces. Of the two you mentioned in your question, you should use the 25 mm one. It will give you a lower magnification, a bigger field of view (better for most bright nebulae and galaxies due to their often significant angular dimensions)
Here's a highly configurable calculator that you can use.
Since you live in the northern hemisphere, objects from the Messier catalogue are great candidates to begin your observations with.
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