nwillis:
I found a useful article here... http://blog.cuyahoga.co.uk/2012/06/assembling-the-currentcost-interface/ using an XINO board and Ethernet Shield (no MAX232 so I am guessing it is TTL) to push data to cosm (www.cosm.com). Cosm is another site that allows you to upload any monitored data. He also includes a link to his code, and I also found an example in the Auduino examples, so looks pretty straight forward.
Yup, interfacing between the CurrentCost device and Cosm, using an Arduino-alike as the go-between really is that simple. I should know as that's my blog you've linked to 
Accessing the data is a case of doing SoftwareSerial reads at 57600 baud (for my CC128, your Envi might be different, but I doubt it) and parsing for the data you're interested in. Connect to the RJ45 port on the back of the device from your Arduino, send it power and ground and get back the data line - just three wires. This approach also means the device can parasite off your Arduino for power, so you've only got one PSU instead of many (and a PC in your case). Your post has just made me realise I never posted the latest version of the code - I'll sort that out, sorry, but if you're in a rush, an earlier incarnation is here.
As far as the hardware is concerned, you'll want an Arduino-alike with ethernet capability. These days, your choices for that are getting wider every day; Arduino + Ethernet shield, Arduino Ethernet, Nanode, Xino + ENC28J60 shield, Arduino + WIZ820io and probably a whole load of others. Which you chose is probably down to your budget or local availability - that choice then determines which library you'll use to handle the network communications.
You may have success with polling two instances of SoftwareSerial to also get data from your Inverter, or you could use hardware Serial - I'll leave other folks who've been there and done that to comment as it's not something I've played with.