I'm fairly new to the whole illustrating for clients and getting paid thing.

I'm illustrating a book and the publishing company wants me to sign away all the rights to the illustrations to them. Is this okay? Should I ask that they add a clause requiring them to display my name alongside any future publications of my work? Add a clause that they not sell it/alter it/whatever? I assume I would still be allowed to use these works in my online portfolio for example, right? Or should this also be written down in the contract?

I obviously don't want to get screwed over since I have zero experience with this. So what should I pay attention to while signing any contract of transferring copyright? What should I definitely NOT agree to? And what should I definitely be ready to agree to?