Starting Out - Living Rent-Free but Looking to Invest

[Ted T.]

First of all, I'm thankful to have stumbled upon this community and look forward to learning/growing in my knowledge and experience with you all. 

Here's my story: DW and I are living rent-free in a small SFH that I grew up in (my parents own/renovated the house but purchased a house a few towns over and would prefer that we live here rent-free rather than collect rent - yes, I'm incredibly thankful). We have about $120k saved up toward an unofficial "house fund" and are thinking of investing in real estate.

We plan to live in our current place for the foreseeable future as there isn't much incentive to do otherwise, so taking advantage of (for example) a FHA loan doesn't seem to be an option (since we wouldn't live in anything we purchase).

Ideally, we are open to purchasing a SFH down the road if we feel the desire to upgrade, but in the meantime I'm not sure what the best strategy is to start out.

Location: SoCal, family size of 3

Given my situation/location, does anyone have any advice/suggestions in terms of what types of properties to look for (i.e. apartments, duplexes, etc), financing strategies, etc?  Any feedback at all would be incredibly appreciated as I am just starting out.  Thank you!