I've completed the Blood on Ice quest, I just don't know what else I have to do. I'm not too far into the main quest line so I'm worried about siding with the stormcloaks and how that might affect the main quest. Do I have to tell Ulfric that I came to Windhelm to fight the imperials to get on his side and to be able to buy the house?
There's an answer to this question: Why can't I buy the Windhelm house (Hjerim)?. In your case, you may have completed Blood on the Ice (but check the spoilers for that quest to be sure...) But this quest is not necessary either for purchasing the house or for becoming Thane of Eastmarch. To become thane, you must join the civil war and complete one of the quests (Liberate Falkreath for Ulfric or conquer Windhelm and depose him.) You must then complete the five quests to help the people of Eastmarch, after which you can buy the house and become thane. I believe you can complete five quests helping NPCs in Eastmarch before even asking about becoming thane, since I've done something similar in other holds. Thus, you could get the tiny quests out of the way before beginning the civil war.
Note also that there are a couple known bugs when trying to purchase Hjerim:
- The option to buy the house may exist but you are unable to actually purchase it even after completing the prerequisites as the dialogue still says it is unable to be purchased due to unpleasantness.
- It is possible that after the Battle of Windhelm, Brunwulf Free-Winter may not appear in the Palace of the Kings, preventing you from being named Thane of Eastmarch and preventing the purchase of Hjerim.
Since you haven't taken sides in the civil war, these do not apply yet. After you complete the appropriate stage in the civil war and are ready to become thane, if you have the first bug, try leaving for another city and sleeping/waiting for five days, then returning to see if the bug has been resolved. If you have the second bug, the wiki describes a fix.
The wiki page for Hjerim mentions that if you have gained access to the house through the Blood on the Ice quest, you can still use the house as a base. You will not be able to decorate the house until you complete the appropriate steps to become thane. There is also a console command for the PC that is reported to give you ownership of the house:
setstage 000A7B33 10.