As an amateur with limited budget, I'd be interested in taking photos of the night sky, trying to capture more detail than human eye armed with a lens of comparable parameters to what I have in my camera normally could see. I doubt I'd ever get down to details as fine as Jupiter's moons, but I'd hope to see detail of some nebulae I have a hard time seeing through my inexpensive telescope, stars too dim to notice in less-than-perfect conditions etc. I'm interested in taking full-sky images just as well as zooms on specific objects too.
Currently, I have a lower-end SLC camera, with two lenses - good sharpness though lower aperture with 50-120mm focal length, and a wide-angle, high-brightness one (about 12-50mm) currently. Firmware hacks allow me to take photos of arbitrarily long time, and I have the remote to start and stop it without touching the camera, and generally software-wise the camera is quite powerful. One of the lenses (the longer focal length) is of "standard professional" quality level too.
Is this sufficient to get started? If so, what kind of settings should I use? If not, what other kind of entry-level equipment would I need to obtain/build on budget to get started with night sky photography?