Godaddy is the scum of the internet businesses. Stay far far away. I was on Bluehost for years, had no problems with it, but my usage was tiny. Note that it's hosted in Mormon country, I've heard that they're rather prudish in some respects.
Most of the "big name" hosting companies do a ~$10/mo "unlimited" shared hosting deal. It's just the generic hosting plan with other resource limitations (e.g. CPU cycles, memory usage, etc.) instead of "disk space" or "transfer limits". These are your generic hosting providers, and any of the establish ones will give you similar experiences, e.g. Bluehost, Dreamhost, HostGator, etc...
You would be fine if all you want is a generic shared hosting and not use much resources. However, with such low resource usage you can probably get much cheaper service from elsewhere. Other services that actually charge you for what you use, or have plans that resemble actual cost better, are able to charge low prices for low usage and higher prices for greater usage rather than averaging it out. If you use less, it's cheaper, if you use more, it's more expensive, but your demands won't be properly serviced by those generic hosts so you'll have to shell out that money anyway.
I was paying $100+/yr on Bluehost, but I've since switched to NearlyFreeSpeech.Net and only pay for what I actually use now, which is a few bucks a year. It is in the US though, I don't care because there's no non-public data on it. There's also Gandi, which is french, it's generally well regarded for their domain registrations but they do hosting too. A Small Orange is in the US, it had a great reputation, I'm not sure if it still does, google around. There's HostPapa in Canada, which is just your generic host akin to Bluehost et. al.