Good question. Most of the big, permanent mounted style generators provide clean power. Clean sine wave pattern for computers. However if you are only using the generator on sparse occasions and have only a small portable type your APC or UPS backup should do a very good job at cleaning the power up from the generator. That is why they have a line conditioner in them. To protect your electronics from dirty, spikey voltage.
Now the internet part is a whole 'nother issue. If you have and ice storm more than likely the internet is going to be disrupted as well. Not always but if a line breaks...your out. Kinda like the land based phone. remember the old school type that just plugged into the jack? Well you'll need one of those too, because if you have the wireless hand held style, those don't work when the power is out. We keep one of the old Slimline phones in a cabinet in the kitchen just for those times...