I know nothing about philosophy--what can I do?

If you're not opposed to free, self-paced, online classes, this might be a good start:
Plato, Socrates, and the Birth of Western Philosophy

https://plato.stanford.edu/ is an excellent resource for philosophy students. You can plug in names or concepts and get well-written, detailed, authoritative information.

As others have suggested, online philosophy courses are a great option.

Another you might be interested in is Peter Adamson's "A History of Philosophy Without Any Gaps" series.

Here's a link to the first volume in the series. It's written in an easily digestible style and makes no assumptions about pre-existing knowledge. I haven't read the first book in its entirety (yet) but will probably go back and take a look when I have a little free time.

Edit: I almost forgot, there's also a podcast by the same name hosted by the author himself! I believe it is available for free. Peter Adamson is a professor of philosophy at the Ludwig Maximilian University of Munich.

I suspect reading their books without any pre-knowledge would be fruitless, or at least very boring.

Philosophy has a bit of a bad reputation for being dry and impenetrable (and philosophers like Heidegger did little to help with that), but quite a lot of the time I find that philosophical texts can often be quite readable if you're interested in the subject matter. Naturally, entire books of Ye Olde English and bad translations are definitely out there and can be tiring after a while, but it's not impossible to get along with.

Is there a good recommended reading list where I can learn the basics of philosophy from the ground up?

So you're not specifically looking at a specific area of philosophy? The recommendations I'd make for someone interested in, say, ethics is vastly different from those who want to learn about logic, metaphysics or epistemology, and someone forcing themselves to read such works could well be turned off of philosophy as a whole.

If you do want a good overview of philosophy without getting too in-depth, I highly recommend the podcast The history of philosophy without any gaps, which follows the evolution of philosophical thought chronologically so you can see where things are coming from and what they're reacting to. I found it to be a great insight after I finished my degree in Philosophy which was more topic-focused and jumped around a lot, often at the expense of understanding the context in which writers made their arguments. The downside is that because of this, it will be a very long time before the series gets to the more modern schools of thought - he's currently in the 15th Century.

So if you're interested in Mill or someone like that, you may want to look elsewhere. A good resource is actually the open courses that top universities make available for free online and most Philosophy-101-style courses will probably be a 'greatest hits' of Western philosophy. I'm a big proponent of the method of starting with a general overview and then diving deeper into the parts that specifically interest you. Don't worry too much about if you're 'qualified' to read a certain book - if it looks intriguing pick it up, and at worst something doesn't make sense but you now know what you don't know.

With that said, if you're looking for a general grounding in Philosophical thought, read Plato. And not just the Republic. There's a great quote by Whitehead that “The safest general characterization of the European philosophical tradition... is that it consists of a series of footnotes to Plato.” The depth of thought, breadth of topics and sheer influence on everything that has come since has made it absolute must-read material in my opinion. Reading Nietzsche, Kant or Wittgenstein will do little to help you understand Plato, but Plato will give you insight into these three and more.

I've been interested in philosophy / ethics since watching The Good Place several times in a row. I'll be taking some of these suggestions up myself. Thanks all!

EDIT: I do have one recommendation! https://www.youtube.com/watch?v=1A_CAkYt3GY Crash Course Philosophy! Might give you a good base to build on. I've watched certain segments of this between TGP rewatches.

There's a podcast I've been listening to lately that might give you the information you're looking for: http://philosophizethis.org/

He basically starts with some of the earliest philosophy in Greece and Italy, then moves forward in time, touching on both Western and Eastern philosophy.

I would recommend listening to the BBC In Our Time Philosophy podcast.

Wisecrack goes over the philosophy of themes in media on their Youtube channel
https://www.youtube.com/playlist?list=PLghL9V9QTN0jve4SE0fs33K1VEoXyL-Mn

My suggestion, if you want to avoid enrolling in a university or community college, would be to watch this video: https://www.youtube.com/watch?v=QkP4g9e86qA

It goes through the major philosophers and philosophic eras of western civilisation. To get an in depth understanding of each of these topics, you now have the key words to search for online or at your local library. Avoid primary sources at first (especially in regards to philosophers of the enlightenment era) as it will be so unlike anything we would write/read today that it is more likely to confuse than enlighten you. Everything from Hegel onwards, and Platos works are exempt, but doing some background research on it can't hurt.