Not only should you look/make an offer on homes 15-20k above your price range, you should lowball the offer. If they don't want to sell to you, screw them and walk away. Don';t negotiate upward. In the current market, only look to buy, if its less expensive than rent.
If the annual rent on a similar house is in the 4-5% of the expected sale price, by all means rent. You will be better off in the long run. Assume you stay in the house you buy for 5 years. You have to pay about 2.5% annually in prop taxes. You'll have to pay closing costs in the range of 9-10% on the round trip buy and sale. If you take out a mortgage (lets say 5 year ARM since in this case you sell in 5 years), you'll still pay about 2.75% annually after tax for the mortgage interest. So, that's a total of 7.25% annually. If the house stays flat (value), you'll lose money by buying the house. Also, keep in mind that if there is any inflation over those 5 years, you'll lose that much as well if the house value stays flat. If inflation goes back to the long term average rate of 3%/year, your house would need to go up by about 26% over 5 years to break even with a rent that runs at an annual cost of 5% of the expected sale price (when you don't include the effects of leverage).