As someone who works in Los Angeles as a film-scoring recording engineer and mixer, I'm more than a little amused at the obsession with the number game concerning 5.1, 6.1, and (!!) 13.1. FYI, there are very, very, very few movies mixed in anything other than 5.1. And if it is the rare 7.1 release, then it is 7.1 for theaters, which is intended for spaces with very wide (40' +) screens that can effectively use the array of 5 front speakers. There are still only 2 surrounds in theatrical 7.1
I contend that your films will sound better with a 5.1 system than a system with more speakers. Why? Well, there'll be less phasing from speakers all over the room, less matrixing (if any) to fill in speakers that were never intended to be used, and more amplifier headroom with fewer speakers means better dynamics and less clipping.
Home theater above 5.1 is marketing, pure and simple. There is no need to fill small spaces with speakers, matrix information into them, and then under-drive them. Spend the saved money on acoustic treatment and an extra subwoofer.