Sounds like you're looking for an Ultrabook.
There are many options, like the ASUS Zenbook UX305LA 13.3-Inch Laptop (5th Generation Intel Core i5, 8GB RAM, 256 GB SSD, Windows 10): Click here for Amazon link (While it's on sale)
Dell also offers a few compelling options, including AMD APU laptops for some of that Radeon Core goodness (Also has Intel options): Take me to Dell
Here is a good link to a video that might help you get started:
Choosing a laptop can be hard, especially when on a budget. Good luck choosing the right one!