well it depends on how involved you want this to get. a 6000w should power everything u need for your home but they will be large an heavy to move by yourself*just something to think about* i would only go with a honda they are stupid quiet you will thank me later when your tryin to sleep.
i personally like the 2000w ones as u can daisy chain them to make more power but are able to be moved by one person which is nice becuse that time will come. you can also cut one off to save fuel as that might be a issue you run into unless you get a naty gas thats hardwired into the system its something to think about. also you can hardwire them into your breakerbox with some work but dam thats nice to have no cords going every which way then having to move appliances etcetc not nessasary but dam usefull and a headache saver!!!
alot of the new generators have build in protecters just like your home. keeping them out of the elements is good for any engine but it wont stop working if u have it outside an it snows/rains just gotta make sure the intake is dry and the exauste is being removed freely. you can use them in a garage but need to know that its sealed from your house as ive seen alot of shotty work that isnt sealed or draws air into the house from the garage sad but true so know how ur system works.
the covered dog house would be a NO in my book due to the fact no free flowing air which would make the exaust go into the intake. but imo it really doesnt matter if its outside just keep the water off it to keep it from rusting like any engine there not any different than your car!!
hope that answered most of your ?'s