If I purchase an Ether for $257, have I purchased stock in a company or just some type of currency? I am all new to this and have no background in stocks or markets so dumb it down for me, please.
If you buy Ethereum, or ETH, you're not buying stock in any company. You're buying a type of digital currency, more often called crypto-currency. Like any asset (gold, oil, euros, etc.) its price can fluctuate relative to the US dollar and does not depend directly on the performance or profits of any particular company (there is no company called "Ethereum" anyways).
With this $257 you would buy 1 ether, one entity of the digital currency which are generated by the Ethereum software/network. Ethereum itself is not a company, its a open source software developed by the Ethereum Foundation. It's possible that this software fails and the value hits zero instantly. (But not very likely) Ethereum is a high risk investment!
Keep in mind that every block (~16s, https://etherscan.io/chart/blocktime) 5 new ether are generated. Ethereum has an inflation rate of 14.75% in 2017 (What is Ethereum's inflation rate? (how quickly will new ether be created))
In 9.6 year from now on, there will be twice as many ether as now. (92318586 Ether / 5)* 16.5 / (3600*24*365))