Re-REmake will by my first time through RE1
You wont regret it. I dont normally play games like these over again and especially in such quick succession but after going through the mansion over and over again, back and forth, evading crimson heads and hunters, conserving ammo and many many close calls I can safely say that this is the best Resident Evil game I've ever played.
Hard Mode is where it really shines, you really appreciate all the balance and thought that went into this game, every time you progress in the game you are rewarded with beautiful haunting backgrounds and subtle music cues.
As a first time player of REmake, I fucking love this game to death.