leash training

So I am looking at all of these cat trees, and I am finding that they are soooo expensive which I wouldn't mind but they also are ugly and not well made! So I am wondering several things: What is everyone's favorite cat tree, or cat scratching/climbing set-up? Cat tree vs. cat climbing walls...

My girl sphynx who is 1 yr and 5 months old has started running out the door when I open it. I am really having to watch her. There are strays in my neighborhood and I have seen them on my porch even. What can I do to help stop this? Should I train her on a leash inside and then take her to safe...