@Darian While 2-3k is quite low for the amount of work involved, for a first book I admit it could be worse and this could be a good opportunity for your career. Nowadays I wouldn't take a book that paid any less than 8k (but min 10k is even better), but I did my first book for 1.5k so I acknowledge that there is a ladder here to climb and I'm not one to try to make artists feel bad when they take a project with a lower budget while attempting to start their career. I think that would be ignoring the realities on the field when you're trying to get your start. It's a tough place to be and I think you should be able to do whatever you feel you want to do get your start, without an annoying pro telling you "Anything under 50k is TERRIBLE, I wouldn't even CONSIDER such AWFUL companies!!" ... That's so not helpful ^^'''
That being said, I'm more concerned with the work for hire part and especially, the TIME FRAME. It seems these people have a tiny budget yet they want it all: they want high quality, a time consuming painterly style, they want it FAST and they want all the copyrights. That's like if I have $2.50 in my bank account but I want an AAA steak cooked by a chef, and I want it in 2 minutes. I think 2 months is not enough for this amount of illustrations in this style. Let's say it's 30 illustrations total, that means you would have to character design, thumb, sketch, tone and color test, and finish painting 1 illustration every 2 days. On top of that 3k is likely not enough money for you to live on for 2 months, so you may have to do some other work at the same time to eat and pay rent. In terms of hours it just doesn't add up. You'd be signing yourself up for one hell of a burnout, if you even manage to hit your deadline.
My suggestion would be to tell them "Look the industry average budget for a 32 page book is 8k to 12k. But this is my first book and I'm willing to do it for 3k. BUT I made calculations (explain to them what I said in the previous paragraph) so in order to be able to create this amount of work in the style you requested and at the quality level you're expecting to see from me, I would need at least 4 months."
Do try to negotiate the budget up a bit. Even if you get it up to 3.5k that would still be an improvement 
Lastly please try to negotiate the copyrights. It is NOT normal NOR industry standard to demand exclusive copyrights for a book. Try to explain it to them. If giant publishers like Simon and Schuster or Penguin don't need exclusive rights, why do they think they need them? And these copyrights are EXPENSIVE. If they do actually need them for a legit reason (like making merch to make more money) they why do they think they do not have to pay additional for this extra, non industry standard thing they're asking for? They may not budge on this, and I'm not saying you should absolutely refuse the project if that's the case. Do what you feel comfortable with. At the beginning of my career I accepted work for hire contracts and I couldn't care less about it because I had bills to pay and I did what I had to do. However it's worth discussing with them. 99% of authors or small/newish publishers think they need all copyrights (for some reason) when really, they don't. They don't realize that it's not the norm. And in my experience, informing them that this is not industry standard and that none of the successful publishers do it is the biggest argument for them to reconsider it. They're like "Oh, it's not? Oh, pros don't do it? Well.. like I'm a pro too, so I guess maybe I don't want to seem like I'm not as informed as I thought I was...." Best case scenario, you might change their mind! Worst case scenario they don't budge, but at least you tried.
Good luck and do keep us updated!