CTs would be the easiest option for longer term monitoring. Installation is non-invasive (to the wiring), and you can either buy a power monitoring system or design one yourself.
For something portable and non-permanent, a current clamp can be used to monitor a single device.
For a quick check, you could use a kill-a-watt
If WiFi worked before, there’s no reason it won’t work with a new ISP. It may be that the router provided by the ISP is crappier than your prior one, just buy your own router or AP