Get yourself a 1-1/2" to 1-1/4" adapter for the drain stub, and then you can go 1-1/4" all the rest of the way. As for the bottle trap, while they look stylish, they are not code compliant in many areas of the country. In addition, unless everything aligns perfectly and the wall connection is exactly centered behind the drain stub with the fitting exactly 90 degrees to the wall, it can be quite difficult to get a bottle trap to fit properly and not leak. I considered a bottle trap for a recent bathroom reno, and ended up being glad I didn't. I'm pretty meticulous, but my sanitary tee was a hair out of square with the wall, and I wasn't ready to cut it out and try to replace it. Standard P-trap installations are much more forgiving.