Please tell me what I should look for when buying a baby browning? Any better variants? Good or bad about these?

There really aren't any variants.  Make sure the magazine is an original FN magazine and try to find one with the pleather pouch.  Those items are worth quite a bit and hard to find other wise.

There is an alloy frame version that is scarce...but most of them will be the "standard" configuration.

I own two, try to get one with the serial number starting with at least a three. As in 300,000 and below. The ones with the higher serial number have polymer triggers and mag catches, the other ones are all steel. Great little pocket pistols, I consider them among the best designed.
 

Where did you hear this?
I have three Baby Brownings with serials higher than 300,000 (one is in the 470,000 range) and NONE have plastic triggers or magazine catches.

PSA made clones DO have plastic parts.

I have #444XXX and it has the plastic parts. Made in '68.
 

On the PSA baby you can get either a plastic or a metal mag catch and trigger.  Plastic doesn't have to be a negative, FWIW though I''d prefer metal.  On an original gun be prepared to replace the recoil spring and magazine - if it's a flat follower count on it not working.  PSA will rebuild your Baby Browning - the owner Lenn knows Baby Brownings backwards and forwards.  The alloy framed guns tend to sell for more, and really aren't that much lighter.  Anyway, all replacement parts are available.

I'm working on setting up as a sales rep for PSA in VA so if there's any questions regarding a new gun or rebuilding an original let me know (or send an email).