So I've started a new character. A pure mage who's not going to join The College of Winterhold until late in the game. So I need to buy a house for safe storage and all that good stuff. My favorite one is Breezehome. But then I have to start the Main Quest and then the dragons will be loose. I'm not going to use fast travel at all on this character. Unless I get myself stuck or something. So my question is this:

Do you get a lot of random dragon encounters even if you don't fast travel?

Uh huh you do. You can get a house in Sollitude without touching the MQ though.

Wouldn't you need to do the Civil War quest first?

You can get the Breeze Home without unleashing the Dragons if I'm not mistaken. If not then try the other cities for one you like.

you caould just get married and use your spuses home, or theres these -

Free Shacks
There are several empty shacks around Skyrim, which contain a bed and a few non respawning containers.

• http://www.uesp.net/wiki/Skyrim:Alchemist%27s_Shack has an endtable as a container. It also has the benefit of an alchemy lab.
  
• http://www.uesp.net/wiki/Skyrim:Meeko%27s_Shack has a barrel and an end table for containers. However, the barrel respawns and so do the shelves, regularly filling the house with junk.
  
• http://www.uesp.net/wiki/Skyrim:Riverside_Shack has one safe wardrobe and a bed. See http://www.uesp.net/wiki/Skyrim:Containers#Safe_Containers for more details on safe containers.
  
• http://www.uesp.net/wiki/Skyrim:Traitor%27s_Post has two wardrobes and a cupboard that you can store items in. The chest there resets along with the bandits.
  
• http://www.uesp.net/wiki/Skyrim:Lund%27s_Hut, north-northwest of Rorikstead, is a farm house with non-functioning bed. Only the chest and end table are safe containers.

Yeah, I know about those but I want to have a proper home and not worry about things resetting all the time.

Not sure, I know you do things for the Jarl (high queen) There are houses available without doing the MQ I think though.

Well, yes, Honeyside in Riften being one. But Breezehome is still my favorite

Ew, I hate breehome lol, its small and cluttered. But I guess its personal choice
I tried making a mod with improved interior to my tastes. It never worked right :'( lol

The house is decent but I really like it's placement and the town

Breezehome is the only one that you have to do (part) of the MQ to get. The Markarth house is my favorite. My thief uses Honeyside and it's ok. The Solitude house is just to big and doesn't have storage were you'd want it or even nearby, course neither does Honeyside. I never did get the house in Windhelm.

I hated the Clutter in any of the houses I buy so one of the first thing's I do is go around and remove all the food that is left out and put it in storage near/in the kitchen area. All the "wicker" basket's go by-by. I do put Apples in a bowl on the kitchen table.

You get a lot, but save regularly and run towards other NPC's if a dragon appears, giants are a great place to go to as they will take aggro and kill the dragon for you. If no npc's are around, keep ducking and diving behind cover. follow these rules you should be totally fine against them.

You can get Breezehome without starting the main quest. You have to "win" the stormcloak side of the civil war though. The new Jarl will give you Breezehome without completing the dragon quest.

You can stop at the point immediately after fetching a certain item for Farengar Secret-fire and before traipsing out of Whiterun for a picnic with Irileth and friends. At this point you are allowed to purchase Beezehome but is not yet a Thrane served by She-who-is-sworn-to-carry-your-burdens.

If you want more specifics, you should have posted in the spoilers section.

Fire/frost resistance are your friends against dragons. It also helps to be able to take a hit or two if they get their bite attacks off. While I used to try to avoid dragon fights, I seek them out now, especially if it's a dragon fort with a word wall.