Realistically if this were to happen I'd stay at home. Much though I love the idea of heading into the woods and building a shelter away from everyone, etc., I don't see many advantages and I see plenty of disadvantages. Priorities: shelter, fire, water, food...
Shelter: a house, a nice warm duvet (or 3), a comfortable bed
Fire: a good wood burner... I live in the country so I'd use dead fall first and cut wood as sustainably as possible if necessary to ensure a future supply... loads of matches, several firesteels... FBF if need be after that. Might find some good future bow drills and bring them indoors to thoroughly dry them in advance. Car battery is another option since it'd no longer be required
Water: Short term outdoor UV-style, would probably have to resort to filtration / boiling long term
Food: Short term use the supplies in the house (I'd guess a few weeks worth), medium term hunter gatherer. Don't forget that cattle / sheep would now be butchered locally, possibly in-house as they were in the not too distant past... Long term the garden would be improved and extended, possibly keep some animals too. Chickens, pigs maybe... turn it into more of a farm?
With a house full of electronics it would make sense to use them. Motor to improvise a hydroelectric generator in the river, run some cables up for lighting / kettle as priorities...
The internet and this computer could be a valuable resource, but of course the internet would be down so I'd rely more on the books I have here for information.
I think the sociological aspect is an interesting one. I'd obviously try to help the neighbors, and the idea 'two brains are better than one' would be valuable for innovation. On the other hand though there is the potential of disorder and looting, though around here I would think that'd be fairly limited. If any city folk manage to walk their way here I can't imagine there'd be many left in a fit state for a decent fight
I would probably keep some kind of weapon around though for self defence just in case...!
Really interesting and thought provoking topic. In a way I'd almost like it to happen, just to see what it would be like!