TongFang makes several laptops with AMD Ryzen processors and Radeon graphics that work well with Linux for well under uiur budget. The PF4NU1F is supposed to be a good one.
https://laptopwithlinux.com/tongfang-pf5nu1g-amd-ryzen-is-no... sells a version under $800 USD.
There are many other companies selling rebranded TongFangs with various configurations and prices; spend some time finding a good one.
An even better option is to buy used/refurbished. Used ThinkPads are a solid bet. See if you can find someone selling laptops nearby, in your area; you'll be able to hold/inspect/use/open it before you buy.
If you're not using Windows/macOS then avoid Nvidia. Handling their driver issues is a nightmare. With Intel and AMD, you basically never have to think about drivers.
For good official support, Lenovo officially supports upstream Fedora on some of its laptops. System76 and Slimbook are other good options for "official Linux support", but System76 can be pricey. TongFang laptops have a community of Linux users to help, but you won't get much "official" support.
For a very low-budget ARM laptop, the Pinebook Pro is a great option with lots of community support. Don't expect to play 1080p video on it without a few framedrops, though.
One of the biggest battery hogs is video decoding/encoding. If you plan on watching online video, your device should ideally support good hardware-accelerated VP9 decoding. AV1 might also be popular in a few years. That would mean that Braswell-and-older Intel chips are out.