Trying to find a "perfect string" is a huge red herring. How do you know you have a half way descent guitar, or pick, or proper finger nails, or technique?
If you cannot do barre chords it could be the action on the guitar, in which case no string will feel good. But you should also know that it talestakes years to develop proper technique and feel in the hands. Once you get it right you won't remember how or why you couldn't do it but you need patience. Even itif the guitar is set up beautifully and have a good quality set of light gauge strings you might still have trouble getting a clean sound on some chords until you've put in the 10k hours of practice.
As a comparison, I use medium gauge Martin bronze strings on my 12 string and strum with all my might at times (for example playing Pinball Wizard by The Who) and never break a string. It might help to know where they break (if and when they do). If it's at a certain fret then they frets need filing (to be dressed). If it's by the bridge then the grooves for the string might be too sharp.