A Protectli FW2B with 4G of memory and a 32G or 64G SSD is 200-ish and probably as low as you can get if you want to buy new.https://protectli.com/product/fw2b/Used mini PCs from e.g. eBay are an alternative. Just make sure there's a PCIe slot for an additional network interface (or 2 interfaces on board to begin with) and the interfaces are Intel, not Realtek!
that´s a arm device, go for x86have you searched, one of the most asked questions...anyhow, any old pc with a extra nic(intel) will workor aliexpress..there are boxes under 200$ that will work
You don't need four ports. An unmanaged 5 port gigabit switch can be found for 20€ or less.https://www.mediamarkt.de/de/product/_d-link-dgs-105gle-desktop-switch-5-2777423.html
Missed the LTE part, sorry. Then buying used is probably the only option to meet your price limit.