If Illustrator is way over your head, Indesign has a workflow that's much easier to learn for someone unfamiliar with the process. Illustrator pretty much designed all of their own tools and "workflow theory", so it is a steeper learning curve than Indesign, which can be (relatively) straightforward.
Indesign is definitely more limited than Illustrator, but if you're aware of the limitations, its likely that they won't really impact your work, from the sounds of it.
Others will probably disagree about this, but I'm being a realist in saying that Indesign will be more than enough for you, and you will be more likely to produce the final product that you are looking for. (in my opinion...)
But now that I think about it, if you're only making one logo you're probably not going to put the work into learning how to do it well, so I guess you can just use whatever the hell you want.
