Low Budget Astrophotography?

What's the cheapest method I can use to produce decent pictures of our solar neighborhood, well enough to see the rings of Saturn? I have a Nikon D5300

It's more about value, not cost. Something might cost more, but give you better value, since they do the job you want it to, with little fuss.

Also, a webcam - either modified or made for - planetary imagine is better than a DSLR. Which gives you a decent value for the cost.
http://www.universetoday.com/108692/from-webcam-to-planetcam-planetary-imaging-on-the-cheap/
www.scienceandastronomy.com/wp-content/…

You can then capture a few seconds of video and then pull out the best frames, then stack those for a decent image.
http://www.skyandtelescope.com/astronomy-resources/astrophotography-tips/how-to-process-planetary-images/
starizona.com/acb/ccd/advimagingplanet…
http://www.cloudynights.com/page/articles/cat/articles/webcam-imaging-with-small-telescopes-r2786

Overall, an 8" goto SCT on an equatorial mount gives you fairly decent performance. Easy to setup, lightweight, compact in size. These make for ease of transport and storage. Some downsides of an SCT include longer cool down times, and image shifting while focusing.