I will talk about publishing as an undergraduate in a general sense. This may change depending on your field of study, where and how the work is published(journal, conference, workshop, etc) and what your level of contribution to the end product will be.
Let's start with the easy question. "Is this good for my career?" I don't know of many fields where having published work, perhaps especially as an undergraduate, is a detriment. As an undergraduate with two publications as first name (in my field the student/person who contributed the most / drove the ground level work is first name, the professor is last name and the names in the middle can range from "was vital to the success of the paper" to "they pushed a button a couple of times") and several acknowledgements having those papers gave me a definite leg up against my peers when it came time to search for jobs. Having publications under your name can be invaluable if you choose to apply to grad school but companies are often very interested to see what high-level, field-acknowledged work you have completed. It definitely makes you stand out in a crowd.
It may seem like nothing but puppies and rainbows but there's a darker side as well. Academic publishing is a lot of work. Depending on your level of contribution this can mean weeks of brutal work rerunning experiments, tweaking inputs/outputs, editing and documenting. Most of the people I know, their first paper was a brutal experience because Academic writing is unlike any other writing you have done and there can be a steep learning curve in both the technique and the tools. So, unless you have a burning desire for a publication for publication's sake, the deciding factors for you should be:
- What is my expected contribution?
- How and where will I be credited?
- What are my obligations if the publication is accepted?
Let's break these down.
What is my expected contribution?
In my field a couple of professors coming up to you after the fact and saying "We are looking to get this published" is a bit weird. I'm assuming that these professors were in some way involved in the work as mentors or that this an extension of their work. It is unlikely that this work is fit to be published in its current state. That's not meant as a slam towards your work, rather it's a response to the specifics of publication. Academic publication is often fairly stringent in style and method. It is likely that parts of your work will need to be tweaked or polished for publication(this really depends on your field to be honest) and, in some cases, completely redone. It is very important for you to demand, in a nice way of course, a roadmap for what needs to be done to get this work published and what you will be expected to do. At that time you should also try to find out how much of the final publication will be your work vs work from others/the group at large. If you have graduated and are starting a new job or heading off to grad school you may have other demands on your time. Writing an academic publication, especially your first academic publication, can be a serious time sink. This will play into the next part...
How and where will I be credited?
Is your work going to be placed, whole cloth, into a template and submitted? Then you should expect to be first author(or your field's equivalent) and be given an appropriately large share of the credit. Is your work going to be used as a subsubsection, comprising all of 2 lines in the final publication? Then the credit to you should be, appropriately, smaller. But that's simplifying things a bit - author order and credit/acknowledgements should be explicitly discussed early in the process. Get it out on the table and nail it down because differences in expectations can definitely damage professional relationships which, to be honest, is probably the most valuable thing you will get out of this. Things like original contribution level, publication writing/editing contribution level, and time/effort commitment to the project should be taken into consideration. Additionally consider your future plans - are you planning on publishing again? Are you looking at going to grad school? Depending on the answers to these questions you may find that the most valuable things you get out of publishing are the experience of publishing and the strong network connections you forge with your coauthors.
What are my obligations if the publication is accepted?
This is the final piece of the puzzle. If your publication is a conference or workshop piece then someone will have to present at the conference/workshop. It should, ideally, be one of the primary contributors. If that person is you, will you be able to attend? Who will pay for travel and fees? Even beyond traveling for conferences/workshops - Who will pay for submission fees? Recently one of my papers was 3 pages over the limit (the conference accepted longer papers at a fee for each additional page up to 5 additional pages). This cost almost $400 (on top of the original submission fees). If this occurs who will pay? If the publication is accepted what does that mean about your ownership of the results of your work? If additional work is done on the project how will it be funded? It is likely that your professor(s) or your institutions has grants for all of this. But you need to find out before you agree to anything. Finally, the question a lot more people should ask, what happens if the publication isn't accepted? Will you be involved in making changes and attempting a different venue? How will the group handle revisions (which, with finished work, can be brutal as you're coming back to the submitted work several months after it was submitted and making changes)?
All of this might seem like a bunch more questions to ask than answers but, really, that's the point. There are plenty who will disagree with me but, in my experience, the research was the easy part. Publishing is the hard, nasty, and occasionally obnoxious part(though it is pretty awesome too). In order to make the publishing part easier you need to have a clear plan for how you will turn this work into a publication and what everyone's expectations are.
I both love and hate my publications. As an undergraduate they gave me a definite edge over my peers in both grad school applications and the job market. I ended up with some very strong connections in my academic community that I can still leverage today. I am still involved as a researcher in my lab. On the flip side my first paper was a special kind of hell. It was two straight weeks of 20 hour days as we pushed to turn finished work into a publication before the deadline. I didn't sleep at all for the last 3 days of the push. My second paper was still brutal, but overall much better as I had passed the worst of the learning curve. I actually got some sleep leading up to that one. I'm incredibly proud of my work but, to be honest, doing those publications pushed me away from graduate school. They were a valuable experience in the world of academic publishing which, it turns out, is not something I enjoy enough to make it my career.
TL;DR: Make a list of questions, email/meet with your advisors/mentors, and flesh out the answers to those questions. If they're largely satisfactory - go for it!
EDIT Given your additional information. Unless they mean publish it on webspace they(or the university) controls OR as a book there is almost no way I can see a 40k word transcript being published as is. My rough estimates put that to be about 100 - 120 pages. I've not seen more than a handful of published papers (etc) over 20 pages long and most are under 10. This may mean they want to publish a portion of it or an heavily edited version of it. This adds a new question for you to ask, what do they mean by 'publishing'?