Custom Domain and host it with BloggerIf you host it with Blogger, you will not need to pay for hosting fees, but you will not be able to upload non-image files nor have the option of FTP access to your blog content.
Custom Domain and host your blog with a third party webhostWith this option, you will be able to upload non-image files and have FTP access to your blog content. However, it will mean that you will have to pay monthly or yearly hosting fees, and at the moment, you will not be able to use the New Blogger template with its new features.
One of the web hosting company you can host your blog with is Fusepoint, a Canadian web hosting company with offices and data centres in Vancouver, Toronto, Montreal and Quebec City. With Fusepoint, you will get better support than the slow and hard to get support from Blogger Support. Fusepoint claims, among other things 24/7 Real Time Customer Care.
So if Blogger Support slow or almost non-existent customer support is bugging you, you can probably get better service from Fusepoint.