I'd say go for a 15" laptop with a Ryzen 5 4600H or 4800H and a GTX 1660 Ti or RTX 2060.
There are even models with a high-refresh-rate Adaptive-Sync display that might be still in your price range: ASUS TUF Gaming A17 FA706IU (17" 1080p 120Hz, GTX 1660 Ti) and ASUS TUF Gaming A15 FA506IV (15" 1080p 144Hz, RTX 2060).
You can normally save a lot of money by buying the 8GB configuration and adding a second 8GB module later yourself, compared to buying the configuration with 16GB of RAM.