I am planning to go the backup generator route when I have the money to do it, ASAP. Power around here has been a lot better since Sandy, the utility companies have done a lot of maintenance since then with trees and we also aren't seeing the dips and such I had been seeing (it was so bad at one point that surges and dips routinely were killing equipment like my router, put it on a UPS for that reason).
You can't use heating oil in a diesel engine for the road, besides being dirty, it is also illegal to use something in a road vehicle that doesn't have road use taxes......(not that I care personally), but more because it is dirty (happiest day in my dad's life was when the old oil furnace went out the door in pieces).
I suspect the problem is the sine wave output of the generator, computers and such can have problems on backup generators, it is why they offer inverter generators, it is a lot cleaner. You can get some of the same thing with a UPS unit where the power is continuously fed off the battery and inverter (bypass UPS units feed line power through and then the battery kicks in).
With an automatic backup generator, it depends on your needs, but I agree given that most of the cost of this is the installation cost the difference between a 12kw and a larger one isn't much last I checked (what prices are now, who knows?) and it is worth sizing up. When they wire backup generators there are a couple of ways to do it, they can wire it into critical circuits only (like heat, sump pump, well pump, refrigeration), you can get one big enough to handle your typical demand (all circuits), or you can wire it to all circuits but if your demand exceeds generator output it is set up to shut down less critical circuits. Me for the difference in cost, I would prob get a 15-20 kw unit (we don't have central ac at the moment, had years ago but decided to forgo replacing it given other priorities, will have it done sometime in the near future.
If you do stay with a 'portable' generator, it is relatively easy to convert it to use natural gas. You would need to get a plumber to create a natural gas outlet on the outside of the house, but converting a generator to natural gas and getting that line outside would be a lot cheaper than a whole house automatic backup.