The best bit is if you die to two zombies at once because they thought pretty far ahead.

At least you started with a great one tho.

I'd say get the original RE2 as well. Preferably the Dual Shock/PC/Dreamcast/Gamecube version so you get some extra features.

Then get RE4. That game's fuckin fantastic and Leon's in that one so you're in familiar shoes. Plus RE4 Leon is Leon at his absolute sassiest and I love that.

The Store also has Resi 1 Director's Cut but since the US Store has the Dual Shock version of Resi 1 Director's Cut, you get stuck with a rather...bad replacement soundtrack compared to the vanilla and previous Director's Cut version. I mean hey why not?

Skip the original RE if you can play its remake. Trust me you're not missing anything as it didn't age very well and the controls are a bit tedious. Plus, that dual shock version's music is ear bleeding.
The remake is much better and just as challenging (if not more with the added Crimson heads and Lisa).

I actually encourage people to experience the original Resident Evil before its remake. The remake actually uses what you remember about the original Resident Evil against you and it's kinda awesome.

I don't recommend that at all. The first resident evil games did not age well. I doubt many people under 30 could put up with the horrific tank controls and hilariously bad voice over for more than an hour.