I recently bought a cheap PTZ webcam from eBay which I was amazed you could get for under £30 and had some fun setting it up as a webcam for watching Poppy.
Search for wireless ip camera, buy it now, In the UK, sort by price & postage, and buy the first one that looks like this (there’s various colours available):
It has built-in wifi, ethernet, microphone, speaker, infra-red lights to see in the dark. And you can control it remotely!
Set up is not for the non-technical, and the manual (if you get one) is likely not very readable, but if you enjoy networking you’ll be fine. It can be done just thru a web browser like configuring a router, or you can try to use the software supplied. I think it advertises a public wifi access point by default, so you can connect to this and browse to its IP address to configure it (give it your wifi details). If that doesn’t work you can connect it to your router over ethernet and you should find it on your local network.
Once you can access it on your LAN, you can get an app on your mobile device of choice. Most IP cam viewer apps should work, my favourite free one was CamViewer for iOS – it’s free and you can control the video full screen by holding corners of the screen. When you hold it portrait you can also do audio, change resolution, etc.
You can access it from anywhere if you set up port forwarding on your router to direct a port on your public IP to your cam’s IP. If you have a dynamic IP you need to use some kind of dynamic DNS provider such as no-ip.com or dyndns.org or the freebie one that might come pre-setup and written on the base of your camera!
You might want to set up a custom webpage where you can view and control your camera. There is help for you in the form of DigitalHam. This guy figured out that the camera accepts control requests at a specific URL where you supply username, password, and control param. His demo cam example is here. I made one too but the cam is offline most of the time now. View source to check it out.