Secondly, saxophone is easier than clarinet.
And more fun.
I second that. Especially if you have big hands. I played clarinet for a few years at high school and I always struggled to get my fingers in the right positions to completely cover the holes (a must if you want the notes to sound right) - thanks to have fairly large hands for a girl. Then I picked up the tenor sax as well and it was pure heaven.
Also, if you want to learn a brass instrument, you might want to start off with something that at least has some keys
(though I remember - my sister could do a bugle call on her clarinet )