Light pollution is a pain but can be circumvented to some degree, depending on your field of interest. Planet imaging doesn't suffer from it at all. Neither does solar imaging, obviously lol.
DSO's suffer from LP more than anything else, some types more than others.
Nebula contain gases of specific wavelengths. For one shot colout, LP filters can help here to pass the wanted light and reject unwanted wavelengths. They come in different strengths from something like a gentle Baader Moon and Skyglow filter, to something more medium like the Astronomik CLS, Baader UHC-S, Lumicon Deep Sky, to a heavy Astronomik UHC. LP filters can have a colour shift and may be tricky to get neutral colour.
After that there's narrow band imaging. Can't be done with an unmodified DSLR. Best done with a dedicated mono CCD camera. Narrow band Ha can even be done in full moonlight. Narrow band filters are expensive. At this stage it will cost a few $$$ to get something decent going but will have the best chance of cutting through LP.
Edit, only took me an hour to type this up so have been beaten in the mean time lol.