The entry level Pilot, Parker and Lamy pens are pretty reliable, for between $20-50. I started with a Parker Jotter medium nib years ago, and it remains one of my favorite writers.
(ed: I’ve had magnificent $3 chinese pens, awful $3 chinese pens, and some that can be improved with fiddling. Most Americans prefer broader, more “buttery” writing, which can be hard to get from the average Chinese nib. For most beginners, then, I’d say get a basic medium nib pen from an American/European/Japanese brand.)
If you're just looking to dip a toe in the water, Pilot Varsity is a disposable fountain pen that can be had for $2-3 in the US, though it's usually sold in multi packs. IMO, it's a decent writer for the price (and the only disposable I've tried and would recommend), and lasts long enough to see whether you'll get comfortable with the way a fountain pen behaves.
Refillable pens can be had for not a whole lot more, but the ink reservoir will be smaller, so, even though they usually come with a free cartridge or two, you may end up wanting to buy a few extra cartridges or a bottle of ink in order to get enough writing time to really get a feel for the pen.
Lamy Safari and TWSBI Eco are two popular starter pens, both around $25-30. The Lamy takes cartridges and the TWSBI is a "piston filler" with a reservoir filled directly from a bottle of ink.
On the slightly cheaper side, the Pilot MR is usually a bit under $20. It's more of a traditional fountain pen look. Pilot Metropolitan is a common name for it (or more specifically a type or MR, just different color/pattern options IIRC).
Then there's all the Chinese pens, some of these are fine but it's hit or miss. I'd suggest sticking with a known manufacturer for a first pen since they have better quality control (especially on the nibs).
Be wary of buying pens on Amazon, their counterfeiting problem extends to fountain pens. Pen retailers like JetPens or Goulet Pen Company are safer since you know they're coming through the real distribution channel.
(ed: I’ve had magnificent $3 chinese pens, awful $3 chinese pens, and some that can be improved with fiddling. Most Americans prefer broader, more “buttery” writing, which can be hard to get from the average Chinese nib. For most beginners, then, I’d say get a basic medium nib pen from an American/European/Japanese brand.)