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I'm aware that some emulators are very specific about console BIOS version (like PSX mednafen)

Others don't SEEM to care much (like ePSXe)

I only intend on running NTSC U/C games on PCSX2 but as I need to buy a PS2, I would like to know if there is a "better" BIOS version to watch out for while I'm shopping around

Or dose PCSX2 not care much about the version? Are there specific games that care more than others about BIOS version?

Not really.
The only one that could give you problems is the very first Japanese one, but it's practically impossible to find in stores

I dumped my PAL bios but a lot of my games are NTSC (friend in the US gave me a ton of games).

I've never had issues running NTSC games on a PAL bios, I also had a friend come over and we dumped his NTSC bios and tested PAL games on it, no issues. I just stick to the PAL one since it's the console I have but you should be fine with pretty much anything.