asics for sure!!! I run daily and those are the only shoes I wear. You said you have a high arch, which might mean you are an underpronator. You can take a quick test to see what type of pronator you are at this website:
Your Foot Type?!?! - A Simple Test To Find Out | TheFinalSprint.com - Track & Field, Marathons, Racing News, Training Advice, Elite Athlete Blogs, Interviews, Podcasts, Videos and More!
If there is a Fleet Feet store near you, I would definitely check it out. Most of the people that work there are hard core runners themselves and know a lot about good shoes. Plus, they make you run around in the shoes before you buy them to ensure optimal fit/comfort.