Some WiFi cameras are also POE. You’ll have to look at the specs for the models you are interested in.
You can just connect to the router for now. And you can use the camera’s remote access app alongside a recording app such as Blue Iris or Sighthound. I use an Android app for remote access and Sighthound for recording.
Yeah, just saw that both cameras also do POE, but I’m glad to hear you can use the app alongside Sighthound.
Okay, ordered the Foscam R4. Should be here Tuesday (Love Amazon Prime!) I’ll let you guys know how it works out. 
Camera seems pretty nice. Didn’t realize it was an “indoor” camera, so I’m not sure if it’s POE, I can get Blue Iris to recognize it with ethernet, but not with wifi. Any suggestions?
Should be easy enough to check, just look in the manual.
I don’t use blue iris, so can’t comment on that specifically. But did you first login to your camera with the web admin interface and enter your WiFi network credentials so it can connect to your router/access point wirelessly?
I don’t use Blue Iris either, but what @marktheknife said is what I was thinking. As long as the camera is on the network, I wouldn’t think Blue Iris would care if it’s wireless or wifi. The IP assigned to the wired connection is going to be different than the IP assigned to the wireless connection. To confirm if your camera is connected to the network wireless, enter its IP wireless address into a web browser and see if you can connect to it.