What other saws do you have or plan to buy? Do you expect to have power saws, or will you be working only with hand tools?
Do you mean you want to use one saw for both rip and cross cuts? Ripping with a crosscut saw is extremely hard work and a rip saw is a lot better at ripping. Crosscutting with a rip saw is much easier in comparison, but makes a rough cut. But … if you buy wood planed to width, most of your handsaw cutting will be cross-cutting to length, although a tenon saw can do a lot of that on thinner pieces.
If you enjoy working with wood, you will end up with at least four saws for straight cuts: a big rip saw, a crosscut hand saw, a tenon saw and a fine dovetail saw.
Massimo, I have a PAX 4.5 tooth per inch (approximately) rip saw that I like very much. I bought it new a few years ago. The handle was a little loose, but I fixed that recently. Remember that if you use saws that you will have to sharpen them eventually. Many people recommend buying a cheap saw (that is resharpenable) to practice sharpening before you try to sharpen your nice saw.
Matt, Northern California - Started a blog in 2016: http://tinyshopww.blogspot.com/
I find a 20in rip saw 10tpi and much easier to use than a 22in saw 10tpi saw, maybe it’s my arm length but the 22in I have feel cumbersome especially of your bench is against wall. That Greaves looks good but I have never used one and it would need the tooth profile changed – very easy to do. The 16in just seems too short. Rgds John