OP you are quite new to the game right? I wouldn't go for a poleaxe right away, I'd try to become proficient with a regular axe or stabbing weapon first. Otherwise you might feel like you're haemorrhaging money on repairs (all are 1k+ every time it breaks) without really being able to use the weapon to its full potential. For me having good ability in all areas (stab, length, swing, shield breaker) is a luxury rather than a necessity, and you pay for it with repairs/slower swing speed.
You could get a Long Bardiche which is basically a Poleaxe but without the strong stab but better swing damage. Or Long War Axe/ Great long axe and you are better than German Poleaxe on the swings (shorter length but its not much). If you want to play a stabbing weapon there are lots of choices, even with shield breaker stat (Swiss Halbard).
So I would get a poleaxe just to try them out when you want, but have some other shield breakers too to use if you feel its not worth the extra repairs while you practice
On topic of which is best though, I think it depends on your style. Poleaxe if you want to stab a lot (and polearm stab is very fast and lethal), german poleaxe for the stronger swings and speed. I never tried Elegant, its stats just don't look that good to me