My favorite is the Acer Spin 513, $180 on eBay (out of stock right now, but they usually restock.) https://www.ebay.com/itm/274884699086

However, to be honest you may want to spend more for 8gb ram and a faster CPU. I couldn't find anything better in the sub-$200 price point, but if your budget goes up to $400 you'll have some nicer options.

Sadly I'm not sure which would be the most rugged, since hardcases for Chromebooks are pretty rare. There are some overpriced ones on Amazon from Chinese sellers, or you could just use a generic case/sleeve. If you could get something like this, it'd be perfect. https://www.amazon.com/Gumdrop-Chromebook-Classrooms-Drop-Shockproof-Protection/dp/B08546JDVK

It's funny, it's so easy to find rugged full-protection cases for smartphones, but for laptops/chromebooks it's so rare.