Zero was just a poorly conceived game all-around. I still maintain that if it had been released as originally planned on the N64 it would be nothing more than an embarassing footnote in the series. Unfortunately, once it got an 'OMGOEEZER MAKEOVER PARTAY!' it suddenly became this relevant entry into the series because it was the same generation as RE4. I still hate that people, after playing RE4, even went back to Zero. Just an awful, awful game... and certainly no way to try to get anyone into the series. It took everything that you SHOULDN'T do with a prequel and, well, did it.
On a related note... I still fail to see, and I only bring this up because I see posts like this all the time, how people have managed to JUST play RE4. Like, I get it, RE4 is great, but how have people (and not just people who were too young) avoid an RE game for the past DECADE? The best is when people go back and play the old games and are baffled when they aren't like RE4. It's not as if RE was this small, niche series or anything... so how have people not played or, at least, didn't even know how different they were? Sorry, random.
Either way, to weigh in on the original question, even though it's likely irrelevant:
Skip Zero.
Play the ORIGINAL. While I love the REmake, it's just... not the same. Part of the joy of the original RE was the low-budgetness of the whole thing, and the fact that they were struggling when making something new. Just the voice acting makes it win.
Play RE2. Fantastic, and the best game in the series, though I'm more inclined to choose the first out of nostalgia.
Skip RE3. Look, it's a completely serviceable game, but it's a sidestory at the core. Sure, you get to be Jill again (yay), and the Nemesis was a very cool addition... but there's just really nothing there. Also has the 3rd worst side character in the series.
Play Code: Veronica. People knock this game all the time, but I love it. The story is a little wacky and doesn't move too much forward, but I just love everything abotu this game. It seemed like a throwback to the first game, and well worth playing, even though it has the worst side character ever. (Seriously, Steve sucks so hard.) IMPORTANT: There IS more plot advancement with the 'Code Veronica: X' for PS2 and GC. There's a whole new bit tacked onto the end that wasn't in the original Dreamcast version.
Skip the REmake. I love it, I really do... but it's also usually frustratingly hard. An amazingly pretty game, but if you play the original, you get enough of the gist of the story for you to understand everything. The tacked on bits (Lisa) didn't work for me, and they made Barry (BEST. CHARACTER. EVER.) look like Jeff Daniels. It's worth playing, but it's also easily skippable, in my opinion.
Now... in terms of picking them up, the only one that should be overly pricey might be Code: Veronica X. It usually hovers around the $30-40 range, at least on the Cube. The original and 2 shouldn't be *too* expensive if you already have a PS2 and just opt for the PS1 versions (original, of course, is only on PS1).
Just my take.