I know there is another topic about house purchasing, but this is my own personal advice!
Good houses in Oblivion are fairly expensive for players in lower levels. There are other topics on how to make money, but if you really feel like having your own place to live, with a nice house, a nice city and a reasonable price - in the beginning at least - take Banirus Manor in Anvil.
When you talk to the current owner of the house, you'll find out it's only going to cost you 5000 gold, which is very cheap for such a fairly big, beautiful house! The trick is, that there is a quest you need to do, as the Manor is haunted and in terrible "shape"! REMEMBER - get a magical or silver weapon before sleeping in the house for the first time. You will need something which can damage spirits is all I will say!
The quest can cost a bit of time and effort (*SPOILER* I found Lorgren Banirus pretty tough in the end, being lvl 8 combat class, but I managed to take him down *SPOILER END*) but in the end, you will get a beautiful full-furnished house for the small price of 5k. As you do the quest, search the room behind the "portal" in the basement and you should find a Tome, which is worth 350 gold, a Weak Potion of Healing, some jewelry, and as you defeat *SPOILER* Lorgren *SPOILER END* a very nice Flame Staff, worth some money!
The City of Anvil is also cool, and I found it a very good deal, as the quest even leveled me up

Now I am saving up for the 20k-house in Chorrol, but a full-furnished house is not bad to have, just to be able to dump my stuff and to feel like owning something.
Good luck!