If you keep an eye out for the next steam sale you will probably get a really good deal on one of the packages.
https://store.steampowered.com/app/57640/Broken_Sword_Directors_Cut/

I would say start out with the directors cut of the first game and work your way through from there. If you like the 5th one you will likely love the first one. The first is the best in my opinion, its one of my favourite games of all time :).