The best hosting I have come across is
www.servage.net (yes it really is that cheap for that much space!)
I've been using them for well over a year now and had no problems, they are great for support and look after you.
As for live one on one chat, you could use Skype? It's free, and you can use it for free skype-to-skype voice calls as well as type chatting.
You can get little icons from their site that you can put on your site and people can click. The only thing is the other person will need to have skype.