I think they must be messing with you, with all these questions about whether you are some kind of ur-INTP. I have known people in all the fields you mention that are of all different types, so it doesn't really matter that much anyway.
I have also known many people with all kinds of degrees that ended up in some other field. What you pick won't define you forever, but it is important because you will have different options as a result of what you pick.
I find psychology really interesting. But it's probably not the best idea due to lack of jobs?
I don't know about the jobs or even much about this field, but I do know that it takes a long time for someone doing clinical psych to get enough unpaid hours (I forget if it is called an internship or whatever), and you have to get through a lot of lean times. INTPs can be very good at this (I think Nathaniel Brandon is one such example) but they tend to get frustrated. I don't know what non-clinical jobs would be an option.
Another option is MIS (management information systems) is this considered a good degree? Even though I'm an INTP I'm not sure working with computers would be the most exciting thing in the world. LOL
I did this job for 7 years and really loved it. However, since that time, I have seen it become more of a blue-collar job, where my job was white-collar. This is not a slam on blue-collar workers at all, just noting that it has changed over time, so be sure the descriptions you see are accurate.
MIS (now often called IT) involves carrying heavy things, waiting for software to load, and crawling under desks. It also requires patience, a problem-solving mentality, and lots of tools. It is a good job for a loner, but does require being able to interact well. My department compared it to being a bartender. People wanted to complain about their day, their boss, their stupid deadline, etc. They wanted us to give them an excuse for why they were late. They were defensive if we suggested they did anything to cause the problem, and sometimes tried to hide what really happened. You have to be a bit of a detective and a teacher in that job.
It also matters where you work. I was in a department that was mostly liked. If your IT department isn't respected, you could end up being very unhappy.
You can always do IT later. Just take the relevant classes, rather than getting a degree. Certification is cheaper and usually better for getting these jobs.
Then there's the science route. Would a degree in chemistry or biology be a good idea for an INTP? Would there be a lot of job opportunities available?
This is what I actually got my degree in, though my science was physics. I never worked in physics, but I have done lots of other things, like teaching, MIS, and accounting, and the physics degree was fine for all of them. I went to a lecture once by Freeman Dyson, about all the things you can do with a physics degree. I have friends with science degrees who have enriched soil for farmers in impoverished places, designed clothing, written video games, and run small businesses.
A science degree is a lot of work and you should really want it before you start one. Any science is probably fine for an INTP, depending on taste. I couldn't do biology because it is gross, and chemistry smells bad to me. Others don't have those reactions. Changing from one science to another isn't as hard as changing from any non-science to a science major.
Any advice on what I get my degree in?
I think you need to do more research yourself, though. Talk to people in various fields. Borrow a textbook and see if it sounds interesting. Ask students currently majoring in the fields you are interested in. Your decision making based on job prospects is sound, so you have already narrowed the choices well. At this point, explore a bit and then go with your gut feeling.
Also, the stuff about needing to like to code if you are INTP is nonsense. I can code, but it isn't super-interesting to me, nor to most of my INTP friends. We all do some from time to time but don't make a career of it. Probably it is worth learning at least one language. My INTJ husband loves it. There are tendencies for INTPs to like to code, apparently, but it certainly isn't an absolute.
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This must be one of the trick threads. "Ho, so you fink you're INTP? Fink again! You die, sir." 
