For an enjoyable introduction to ordinary language philosophy, you may consider:
John L. Austin, Sense and Sensibilia, OUP (1962)

For some more introductory reading on analytic philosophy, engaging yet deep:
Gregory McCulloch, The Mind and Its World, Routledge (1995)
and from the same author: The Game of the Name (1989)

I would recommend the Myth of Sisyphus to add to Nausea, and for a very different type of existentialism you could attempt Kierkegaard.

I am interested in exploring more of the existentialist and nihilist ideas but I will not restrict my reading to any particular philosopher or ideology. I am open to any suggestions at all. — Jamie

I suggest you take a look at some of the discussions and posts from @MysticMonist. He is working his way through Plato. He just started a new discussion - "The Republic Strikes Back: A Platonic Sequel." I am not partial to Plato or a lot of other western philosophers. Is Plato a western philosopher? MysticMonist has opened my eyes, slightly, to the possibility that there is value there.

There is a nice edition of David Hume's Enquiries available free online here.

I am interested in exploring more of the existentialist and nihilist ideas but I will not restrict my reading to any particular philosopher or ideology. I am open to any suggestions at all. — Jamie

The World as Will and Representation by Arthur Schopenhauer. It's imaginative if nothing else. He understands the constraints of human will and freedom more than any other existentially-oriented philosopher in my opinion.

Hi. I think it's great that you can enjoy Nietzsche without agreeing with everything he writes. As I see it, reading philosophy is exposing one's self to vivid, eloquent personalities. They are sometimes a little "crazy" or "obsessive," but their beauty lies in this excess. As we keep reading, we learn to take from them what we can fit into our own, unique lives. We are ourselves become philosophers by trying to fit all the incompatible pieces together.

If you like existentialism, you can't neglect Heidegger. He sees and describes what most philosophers ignore. This short, highly readable book is the best intro I've found: https://www.amazon.com/Heidegger-Short-Introduction-Michael-Inwood/dp/0192854100/ref=sr_1_1?ie=UTF8&qid=1508099015&sr=8-1&keywords=michael+inwood+heidegger

I've recently read the massive Being and TIme, and I'd advise a nice summary to get the gist. No need to bogged down right away. IMO, you should scan around and see what absolutely grabs you. I almost envy you: there's nothing like finding a new philosopher one loves.

If you like what's "morally" radical in Nietzsche, you should probably also look into Max Stirner. The common English translation of his book is long and "baggy," so I recommend a more eloquent summary, perhaps The Self-overcoming of Nihilism by Nishitani. This book looks in Nietzsche and Dostoevsky as well. Dostoevsky's Notes from Underground is amazing, too, especially if you like Nausea. It's another literary philosophical or philosophical literary book.

Thank you for all the suggestions. I have downloaded more books by Neitszche, Dostoevsky, Schopenhauer, David Hume, Kirkegaard and Camus for my Kindle.
Nishitani, Heidigger, Stirner, Plato, McCulloch and Austin are all writers I will check out next once I have read the books I have already.
In addition to these, Nausea arrived this morning and I am looking forward to reading it. I just have to finish Beyond Good And Evil first, but I am nearing the end.

I think it's great that you can enjoy Nietzsche without agreeing with everything he writes. As I see it, reading philosophy is exposing one's self to vivid, eloquent personalities. They are sometimes a little "crazy" or "obsessive," but their beauty lies in this excess. As we keep reading, we learn to take from them what we can fit into our own, unique lives. We are ourselves become philosophers by trying to fit all the incompatible pieces together.

What I enjoy about philosophy thus far, as a newcomer, is that the ideas expressed in philisophical texts provoke thought. Even if I do not necessarily agree with certain points, I can at least understand the reasoning behind them. It is an enriching experience to have your ideas and perceptions challenged in such an eloquent fashion.

Wittgenstein, Philosophical Investigations.

J.L. Borges fictions, if nothing else, his Library of Babel.

The Argentine poet Jorge Luis Borges is not typically classified as a philosopher, but in his short stories he has given philosophy some of its most valuable thought experiments, most of them gathered in the stunning collection Labyrinths. Among the best is the fantasy -- actually, it is more a philosophical reflection than a narrative -- that describes the Library of Babel. — Daniel Dennett, Darwin's Dangerous Idea

I wish I could see the Library of Babel through Dennett's mind.

Books on my kindle that I may read and reread eventually:

Finite and Infinite Games

Mythmaker: A Study of Motif and Symbol in the Short Stories of Jorge Luis Borges by Carter Wheelock

He (Borges) has a superb conceptual grasp of what Wilbur M. Urban called "the natural metaphysic of the human mind" -- the abstracting, god making, fluid, kaleidoscopic world view possessed by primitive men for want of a body of sure and useful knowledge, and the view to which sophisticated men inevitably return when they despair of truth. The philosophy perennis formulates a circular, predestined universe, capricious and chaotic, capable of an infinite number of equally valid configurations; a world in which everything conceivable is true and where "false" can only mean "unthought." Borges looks upon modern men, with their fixed hiearchy of knowledge and an idea of being that differs radically from the loose cosmologies of their ancient forebears, as if they were a choral group that sings only one dogmatized song. — Carter Wheelock

I guess you could have a look at this thread too for choices:

https://thephilosophyforum.com/discussion/1729/your-favourite-philosophical-books/p1

Library of Babel — Nils Loc

It's very short. I remember reading it, and being like :s 'why have I just read this?'

It's very short. I remember reading it, and being like :s 'why have I just read this?' — Augstino

Story of my life. I remember working my job and was like :( why am I doing this.

Story of my life. I remember working my job and was like :( why am I doing this. — Nils Loc

That has sometimes happened to me too - I think it's a very modern way to feel. Somehow in this modern world one cannot really find their place in the scheme of things :s .

What I enjoy about philosophy thus far, as a newcomer, is that the ideas expressed in philisophical texts provoke thought. Even if I do not necessarily agree with certain points, I can at least understand the reasoning behind them. It is an enriching experience to have your ideas and perceptions challenged in such an eloquent fashion. — Jamie

I totally agree. I loved ideas among other things when I was younger. Lots of those other things have lost their charm. But I love ideas as much as ever, if not more. The pleasure of thinking seems to be the most durable of pleasures. It's a passion that I don't believe will ever wear out.

I've also known great friendships, but perhaps my most valuable friendships were "one way." Few living humans can compete conversationally with the great philosophers. They may not hear me, but that's OK. They inspire me to have great conversations with myself --and others who also appreciate and want to emulate these great philosophers. As I see it, we invent ourselves as original philosophers by wrestling with those who came before.

, I agree. While I was reading Beyond Good And Evil, I felt as if Nietzsche was speaking to me and I was speaking to him although obviously he cannot hear or answer me directly.
I am finding these "internal conversations" occurring a lot more frequently since I started reading philosophy. I have always been a thinker and an internal conversationalist, but before I discovered philosophy these "conversations" were mundane.
I have started Nausea and I am finding the themes within interesting. Over the past day or so, I have been unable to devote as much time as I would have liked to reading it due to being unwell with headaches and dizziness so therefore unable to concentrate fully on the text, but I am starting to feel better.