Only the good ones.
Insurance, hangar, annual, etc. I find do vary from one AC to another. Keep in mind that you will pay more insurance for a lower hull value in a twin vs. a single, especially the first year you have. It's important to factor into the total cost of ownership. If you can do your own labor, then yes, you may be able to reduce your costs. However as someone who's mechanically inclined and does all my own work on my cars, I find that I end up paying others to do the work on the planes, and it seems like most other people do. Going into ownership I thought I'd be assisting more in the work. I haven't, mainly due to schedule. I don't see that changing.
Upgrades: yes, those are owner-specific without a doubt. However, what I've found is that when stuff breaks on a capable airplane, the cost to upgrade vs. repair what's there isn't a tremendous difference.
Buying the right airplane will save you a bunch of money in the long run. To do that, you'd be best off hiring someone who knows about the type to assist you in picking out a good breed. Jerry Temple is a well-known guy in the Twin Cessna world. I also have been known to help out people with these purchases.
However, the initial purchase cost will end up being higher for a zero-gripe airplane.
As one of the biggest proponents of multi-engine flight on this forum (probably the biggest - except when Henning is trying to sell his plane), I do understand this statement, and it's a big reason why I fly twins. Last year I flew 500 hours in piston twins, 400 the year before, and this year I've done about 200 so far.
For this philosophy to be effective, you need to be proficient in system failures (which goes beyond just losing an engine). People who maintain proficiency don't make the NTSB reports. An engine fails, they land safely, and they move on with life. It's the people who don't maintain proficiency who have problems. They make the NTSB reports. You need to make sure that you not only get good training, but fly enough to stay sharp and get recurrent training. The tools by themselves don't save you. Danos can tell you about my approach to systems failure training.
You also need to make sure your single engine service ceiling is high enough for where you fly. Your family and gear in a 310 is going to put you close to gross. You would be wise to consider one of the 310s with upgraded engines to give you better single engine performance. If you're crossing various inhospitable terrain, you're really going to want an upgraded turbo model. I'm happy with the upgraded non-turbo model, but I fly in the flatlands primarily - east of the Rockies. In the rare event I fly to Colorado, I accept the fact that in an OEI situation, I'm going down. Being in California, you'd likely have more areas where an engine failure would need extra power.