Hi there!
When we first got Quasar, the house in which we lived was about the size of yours. He did quite well there. We provided climbing apparatus, trees, toys, and scratchers. We are in the habit of taking him and our dog out with us whenever we can. We take him for walks on his harness as well as regular motor car trips.
We moved to a much larger house and I cannot say he does not enjoy the space but he also did quite well in the smaller "jungle".
I will not have Quasar as a free-ranging, outdoor cat for fear of him getting hit by a car, stolen, diseased, poisoned, attacked by cats or wildlife, or simply running away and getting lost. It simply is not worth the risk.
We currently live in a 4000+ sq ft, three-story home and he still tries to escape outside. Occasionally, he is successful but we have not had any trouble retrieving him. He can be frustrating, though, when he escapes. He thinks it great fun to make us chase him.
Best of luck with your little one. Could you post a picture so we can all enjoy?
Cheers!