There is the original series and the recent continuation and three movies. Is there any specific order or can I watch them chronologically?
Berserk Anime is pretty loyal the manga so watching it first is no brainer. Movies are up for grabs, there is no need to watch them if you are watching in continuity since they are basically recap of the original anime.
You should watch the current Anime AFTER the original.
I personally haven't seen any of the three movies, and have heard that the CGI is pretty horrible in action sequences. However, I and many other fans would recommend you to read the Manga (again) after watching the original series. The original series allows you to have a foothold in Berserk. Manga has beautiful artwork and you can skip the Golden Age Arc if it seems boring to you.
If you don't mind the CGI animation, Berserk movies do take the story a bit further and don't spoil anything from the Black Swordsman Arc which the First Episode of the original series does.
TL;DR Since Both movies and Anime tell the Golden Age Arc only they you can watch Either/both, but people mostly prefer the anime even if aged. The newer iteration of Berserk comes after them
If you want to watch the movies in order, it will be Berserk the Egg of the King, then Berserk the Battle of Doldrey, then Berserk the Advent. As for the actual anime series itself, I haven't yet watched it, nor do I read the manga.