Advice Needed for First Investment

[Princeton Brooks]

In my current situation, I'm wondering what I should do.  There is a lot of talk about being at the height of the market and a downturn looming.  I currently live in Los Angeles, CA with my wife and our 11 month old child.  We are renting ($1,500/mo) a 1 bedroom 1 bath "mother in law" suite that we're quickly outgrowing.  As far as debt, we have about $17k at a fixed rate of around 5.5% that we're paying off.  We've managed to save up an emergency fund and extra cash over the years as well amounting to about $58k.  

We've also been pre-approved for $500K and my family would like to begin our investing career, however it's difficult (not impossible) in LA's current market to find cash flowing deals that we have not been priced out of yet.  Which, a lot of times, leaves condos and townhomes as the only affordable options at around $370k+.  These condos/townhomes often do not cash flow but may have potential to appreciate; however, we are unsure if investing now, given where we are in the market, is a good idea.   We are also unsure if buying something we'll have to hold for multiple years before we can invest again is a good idea either if we are unable to find something that can cash flow.  Especially if the downturn occurs during this process.  We would love to invest in LA, but are open to out of state if it makes sense.  

If you were in my shoes, what would you suggest my family do?  How would you begin your investing career...would you wait? Begin? and how?  

Thanks!