So I only have a few Champions currently, summoner level 16.

I have:
Gangplank (Fairly fun, play occasionally)
Fiddlesticks (Hate him, never play him)
Ryze (Not a fan, very rarely play)
Talon (Favorite owned champion, play him the most)
Alistar (Enjoyed him for awhile but I don't really like him anymore)
I had Sion but ended up refunding him due to not ever playing him.

Who do you guys think I should buy? Either someone that would be to my liking according to what I've enjoyed so far or someone who is different than what I've played and what would be good to add to my champ list.

I was thinking maybe Xin Zhao, Graves, or Rengar but I'm open to any suggestions, preferably a 3150 or 6300 champ. I played Xin when he was free and went 30/5/10 in my first normal PvP game with him but that was probably just a lucky game.

Why not just try more of the free week champs till you find some you like? Also, pick up Tristana (you get her free w/ a promo) - she is also a ranged ADC, so as someone who likes GP you may also like Trist playstyle.

I think you might enjoy assassins/burst casters the most. Xin might not be a bad call, as well as strong burst assassins like Leblanc, Kassadin, Akali, Evelynn, etc. A tank you might actually enjoy could be Malphite if you want to branch out a bit - he has low sustained damage, but surprisingly high burst for a tank when he initiates onto an enemy team, so there'd be some parallels to Talon. Cho'gath might be appealing for the same reason, since he does a lot of burst with his full combo, but he doesn't really have any way to rush onto an enemy team when he initiates.

If you go with an AD carry, I'd go towards ones who have high burst like Corki, Graves, Tristana, or Ezreal, since others may feel unsatisfying to you compared to Talon.

My Favorite Champions to play/lane with are as follows, maybe you would like to try some of these out.

(Bottom Lane)- Sona, the maiden of kick ass support, awesome healing and damage support champion

(Bottom Lane) - Corki/Ezrel, The terror of the bottom lane... These two are perfect bottom laners, awesome poke and very high damage

(Middle Lane) - Zyra/Lux/Katarina, The trifecta of awesome mid laners. All three of these champions are awesome mid lane champions and can snowball way way out of control.

(Top Lane) - Spin to Win Garen/Darius/Malphite. Total bad ass tops. These guys are my favorite because not only are they awesome sauce, but they can snowball so out of control!!!

(Jungle) - Skarner/Udyr/Maokai - I dont personally jungle, but when I play normal draft or normal blind I see A lot of people running these junglers and they usually do awesome. Give them a try!

I think the most important thing you're lacking experience in is AD ranged carry( like Ezreal, Tristana, Caitlyn, Corki, and Graves), like a few people have pointed out here. I think you can definitely explore these and they're all fun champions. But I'd definitely recommend you pick up Ashe and try her first. She's only 450ip and the easiest AD Carry to pick up. If you do want to go for a 6300 (by the way, price indicates how recently they came out more than how good they are, so don't worry about that) Graves is a great choice. He's easy to pick up, fun, and you will always be able to use him, no matter what level you're out.
Since you like Talon so much, I'd definitely agree that Xin is a good pick. But if it's the ability-heavy assassin-y thing Talon has going on that you like so much, definitely give Katarina a try. She's very similar and a blast to play.