What do I do with the pets I dont want while still making a profit? I get eggs and then end up with pets I dont particular want. Can I sell them? How would I do that?

You can put a price on them from the "Manage Pet" screen, but be forewarned that pets do not sell for much unless they are extraordinarily beautiful, have good stats, or are themes. It really is not a good way to make money, actually, but you could probably find buyers for 50-100 coins each.

Selling a pet you dont want, especialy a from a wild egg that you didn't get from the lost grove or the festival zone, is a slow process, i would highly suggest to put a 42 days max limit on them, after that time it's best to releass them. This way you save space and gain a small nest bonus for when you get access to the LG, it may not seem like mutch and i know some people dont like releassing but it's a good option for unneaded/ unwanted pets that take gold and space to care for. ^-^

I see, so probably not a good idea to set an unwanted pet for a crazy high price. If selling pets isnt the way to go to earn more gold, what would be?

There is a very thorough player-made guide to making gold you might find useful.
https://www.sylestia.com/forums/?thread=2280
Personally, I would recommend completing missions in Esior's Haven to start with.

A good way to make money... hm... here's a list,
- Selling RARE pets, such as expensive themed and Purebred
- Doing lots of missions. I just find cheap level 70 pets off advanced search and use them in missions. And always increase your mission limit when you have the chance!
- Just playing the map. The higher level the zone and pets you have, the more gold you will get from chests
- Make some friends! I know it seems hard at first but after a while you will have a lot of friends on this game. Obviously, no matter how nice they seem, don't reveal any personal info, but they are good to chat to if you need a gold loan, advice and pets. There is a thread somewhere where you can find a list of people who need friends!
I hope this helped!