Personally I'd recommend using Bitcoin much more than I would WU. Not only is WU a hassle and has additional fees involved, but things just seem to go wrong more often with it for some reason idk.
For buying Bitcoin circle.com is probably the way to go. You might have to get verified, but you just send them a picture of your (real) ID and you're good to go (only takes about a day). If you're worried about opsec or whatever from that just send them to another wallet (coinbase or whatever) and send to g0d from there.
Also when you order from g0d you don't have to worry about BTC price fluctuations. As soon as you place the order he gives you a price in bitcoins, not dollars, so if you have the bitcoins bought already you shouldn't have to worry about coming up short. I would recommend buying and moving the bitcoins to your preferred wallet before you place the order though because your order is cancelled if you don't pay within 30 minutes of ordering.
Also, if the $300 limit on circle is an issue, just have your friend set up a circle account as well. Then each of you should send the coins to the same wallet (coinbase, etc.) and go from there.