I'd go one step further and suggest a Pilot disposable fountain pen. Their nibs are remarkably good, and you're only out around $2 if you dislike them.
And if you like them, well then, have fun with your new hobby!
I was giving away Pilot Varsity pens (a.k.a. V-pens) to people around the office that were interested. Amazon sells them in boxes of 10, and yes they have a surprisingly good nib for such an inexpensive pen. They also have decent capacity, as the thing is basically a non-refillable ink tank with a novel felt feed (similar to what markers use).
The next pen I recommend as a starter is usually the Pilot Metropolitan, or the TWSBI Eco for those who want to dive into bottled ink.
True, I actually did that myself when I impulse bought one at an art supply store since it was at the checkout counter. It's a great way to find out if you're interested in experimenting with pens, or if you just want a no-fuss tool and have a passing curiosity in fountain pens. Do this before getting a non-disposable.
I second the recommendation to try Pilot first, though I haven't used any of their recent disposables. Pilot nibs are just remarkably consistently good. As a starter I'd suggest the Pilot Metropolitan with a medium nib (as Asian nibs tend to be a little finer than European nibs with the same designation) although my personal favourite ‘cheap’ pen (that is, in the Lamy Safari price range) is the old-style Prera (in the US, from JetPens).
And if you like them, well then, have fun with your new hobby!