The first person to buy or invest in Bitcoin is essentially Satoshi Nakamoto, the person (or group) who invented Bitcoin and published the white paper in 2008, and launched the Bitcoin network in 2009.
However, in terms of purchasing and trading outside the founding team, it is believed that the first person to buy Bitcoin from someone other than Satoshi was:
Hal Finney, a well-known programmer and digital currency developer, received the first Bitcoin transaction from Satoshi Nakamoto in January 2009, where Satoshi sent him 10 Bitcoins as a test.
As for the first actual purchase using Bitcoin (i.e., using Bitcoin to buy a real item), it was:
On May 22, 2010, a programmer named Laszlo Hanyecz bought pizza for 10,000 Bitcoins, and this transaction is known as "Pizza Day."