well, I do not think 2 things can be got together. Best and Free... Best will be paid offcourse and Free will not be best. I would suggest you go thru google with the keyword of wordpress hosting and you may get a lot of hosting companies in there. Btw, I can help you get the 6 months free hosting on my paid hosting servers.. let me know.
I don't think that you are going to find anything worthwhile for free, especially not with back ups. If you are just playing around with Wordpress to get a feel for it, then go for it with the free hosting since you have nothing to loose,but if you are trying to get something started to actually try and make some money...you are wasting your time if a free host is the best you can do. Wait until you have enough money to pay for cheap hosting at least and then get started with self hosting. Until then build your writing skills and post count up on Wordpress.com and when you can afford $6 a month for hosting from Go Daddy or somewhere, then migrate your posts to yourself hosted blog and add your monetization. If you find a free host that offers back ups, I'll be more surprised than anyone.