Looks like you got it mostly answered...but I'd go with the home broadband and a wireless card (plus a good firewall!) in the laptop. That's what I have in my laptop and I can use it at my parents, most hotels, coffee shops downtown, laundrymats....etc etc. Using mobile is expensive and not all that reliable, if you think about your mobile phone and how (sometimes) it's unreliable--that's what the internet would be like. My opinion would be that wireless will allow the most flexibility with the lowest price.
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