The Civil War storyline and the Main Quest storyline intersect at Whiterun. You can do the MQ without doing the CW, but not the other way around. If you start the CW quests, once you get to Whiterun the Jarl will not let you advance your CW business until you've helped him and his wizard with regard to the potential dragon threat. But you already know that, and no - there's no way around it. So if you want to do the CW you will have to prgress in the MQ at least as far as taking on that first dragon in Whiterun which will make other dragons start to appear in your game.
However there is ample reason to believe that as long as you do not go any further with the MQ after that, the dragon "problem" will not be as serious as it would be if you kept running the MQ concurrently with the CW. Dragons will be present at known lairs, guarding word walls and the like, but until you complete the Blade in the Dark quest where
Spoiler you and Delphine witness Alduin resurrect a dead dragon, which you then have to kill
it is likely that you will see few to none random dragon attacks (based on the reported experience of many other players). You will have to deal with them if you get too near their lairs but shouldn't find yourself being harried by them in random encounters. YMMV but it seems like a good bet if you want to do the CW but put off dealing with a full-blown dragon onslaught.
Regarding the house in Windhelm, Thenightingalelord is also correct, it will become available much faster if you side with the Stormcloaks since Ulfric is currently in control of Windhelm and can offer it to you as soon as you prove yourself to his satisfaction (that is, complete a couple additional CW quests). You will however need to complete the Blood on the Ice quest before the Steward will sell you the house. This quest is notoriously buggy (altho I've not had any problems with it myself) so it's advisable to read up on it before you go that route. You should be able to link to the wiki page on it from the link in Thenightingalelord's post.
If you side with the Imperials in the war, you will not be able to buy the house until after the entire CW questline is finished, because Ulfric is not going to let you buy it once you've joined the Legion and he will not be out of the picture until the war is over and there is a new Jarl in Windhelm (who IIRC will let you buy it solely as a reward for your military service, but you will still need to complete Blood on the Ice before you can furnish the house and make it livable).