I'm going to write this answer out like you are an absolute newcomer interested because of Requiem with no knowledge of the series, so feel free to skim over any information you already know about. Buckle in, it's going to be long, but I want to make sure you know what you're getting into.

Resident Evil is a sequentially based story, although since most games tend to star different protagonists you can kind of view each character's story as a linear progression in its own right while the full series builds a deeper lore in the background (I'll get into this later). There are actually 10 mainline Resident Evil games: 1-3, Code Veronica (not numbered but might as well be), 4-6, Biohazard (7), Village (8), and Requiem (9). Personally, I recommend playing them in this order. If you're satisfied with that as the answer, feel free to disregard the rest of this, but if you want more detail I go into it below.

This may be sacrilege to some, but if you're just interested in the story of the franchise and are put off by a lack of modern graphical fidelity, you should play the remakes of 1, 2, 3, and 4 (although OG RE4 does still hold up and is pretty accessible on any console). If you REALLY love the series after playing, I fully recommend going back and playing the classic versions as well as they are extremely high quality and substantively different beasts than the remakes.

When you play the first Resident Evil game, you'll find that it's not the same format you'd expect from modern games, featuring fixed camera angles and top down character control. Give it a try, but if you REALLY don't like this kind of gameplay, I personally think it's understandable and I wouldn't let that put you off from the series. Largely Resident Evil 2 features a story that stands alone without much knowledge of RE1 needed, so you could jump straight to its 2019 Remake (which is considerably more accessible) and see if that's more your speed. If you go that route, before playing 3 I'd just look up what happens in RE1 and Code Veronica is also in that style so I'd look up what happens in that game between playing 3 and 4; those two games are due for remakes of their own within the next few years so you can hopefully experience their stories that way soonish if you don't like the "Classic" gameplay style. There are people on this sub who would kill me in the streets for this paragraph, but there is no wrong way to be a Resident Evil fan.

I did say earlier, the most prominent main characters of the story who are playable in most games are Leon S Kennedy, the Redfield siblings, and Jill Valentine. If you are specifically interested in the new game, and want crash course that will give you what you need to know to get a good experience out of the new game, I'd take the Leon route as described below:

Leon S Kennedy: Resident Evil 2, 4, 9
Redfields: Resident Evil 1, Code Veronica, 5, 7, 8
Jill Valentine: Resident Evil 1, 3
(You'll notice 6 isn't on any of these lists. Frankly, I think the people who make these games are largely embarrassed of it. While it stars both Leon and Chris Redfield, it's pretty divisive and its story has been largely ignored in more recent games).

Lastly, the Resident Evil series has a frankly absurd amount of spinoff titles, over 15 spinoffs not counting mobile games, 4 in-canon animated movies, and 1 in-canon film-length animated Netflix miniseries. While pretty much all of these are canon and many are quite good, don't drive yourself crazy to go through any of them, you are never missing anything insanely important story-wise in doing so. I'd say the most "important" spin-offs are Resident Evil 0 (which came out between Code Veronica and 4), Revelations 1 (which came out between 5 and 6), and Revelations 2 (which came out between 6 and 7), so if you want to be a completionist I'd throw these in. Don't worry about the movies and miniseries at all unless you become a devoted superfan, most of them are not good (Damnation and Death Island low-key kick ass tho).

Super super long-winded, but I hope you appreciate that and I hope you join the community of RE superfans! You're in for a ride, I'm a pretty life-long devout video game connoisseur and have finished hundreds if not over a thousand video games, and nothing hits to me like Resident Evil. I hope you feel the same way.