Hi! I'm Scott, and I hope to offer some helpful perspective.
Be aware that I am licensed in Calif. only, work as a general practitioner and not an expert in copyright; but before entering law, I worked in news media and have some exposure to publications sector from that side in addition my recent legal qualifications.
First -- congratulations! You have a publisher's offer in hand!
No, as to the matter of rights ...
A lot will depend on the exact nature of the work and its audience and markets, and your objectives.
Unless you are willing to delve into those aspects, on top of producing the work, you should seriously consider an agent. An agent willing to represent you and your work may well prove to be a key to bids from multiple publishers offering a variety of deals, more or less favorable. The agent's job is to sort through for you based on what you have expressed as your goals and priorities.
The fact that you have a publisher's offer in hand should make getting a agent much easier: yes, yo uwill have to cede some money, but the agent will have incentive to sound out other publishers for you to get a more lucrative deal.
Also, keep in mind that it is unusual for books to sell such that their profits surpass the advance -- few authors ever see royalties.
Publishers at least want to recover expenses, which include your advance, and their costs in publishing, distribution and marketing, which takes time (unless it's an overnight blockbuster!).
Also, "world rights" is a bit misleading, because quite a large part of the world does not adhere to international copyright conventions, so don't be too obsessed with that particular.
So, its going to require an assessment of your goals and potential markets now and in future.
Again, this is where an agent comes in handy.
I hope you found this a little helpful & if so, I would appreciate a positive ration. Thanks and good luck!