For me it's
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Resident Evil 1 (1996)
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Resident Evil 2 (1998)
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Resident Evil Outbreak (File 1 and 2 because it's pretty much one game split into two)
1 will always hold a special place in my heart since it's the first I played. 2 because it improved on everything that 1 did and it was the first Biohazard game I played to completion. Outbreak because it took the series online and introduced multiplayer while still sticking true to it's survival horror themes.
Now's a great time to get into the series since all the mainline games are so easily accessible via emulation or have PC ports. 1,2,3 are all on and coming to GOG.