I know a few people who recently arrived and all found apartments in Kowloon for 10k or less (Yau ma Tei, Ho Man Tin, Mong Kok East). The best thing to do is to get to Hong Kong and go to the area you are interested in and ask an estate agent to show you around. Online searching is pretty difficult as their are v. few cheap apartments that have useful photos or floor plans.
Remember the price is always negotiable so even if they show you one for 11-12k, you might be able to negotiate down to 10k.
A few areas in Kowloon are alot more expensive such as Kowloon Tong, TST and a few others but you can still try.
Majority of apartments will be unfurnished and you will pay more for higher floors, security, lifts etc. I would say apartments have 2 configurations at the size you are looking for. small kitchen and bathroom, decent sized living room and 2 small bedrooms OR 1 decent sized bedroom when the dividing wall is broken down.
Note that the agent's fee is normally 50% of the rent and the usual deposit is 2 months rent.
P.S. I presume you mean 500 square feet, not meters!