If you get a HELOC, that money would be available for you to use but you wouldn't start making payments until you had used the cash.

I then search Zillow and craigslist to see what is available use all this to determine a fair price.

They are portraying renters and showing that fewer homes will be available to them, which seems true as some many on this thread are questioning investing in CA because of this. 

And the available places for renters is pretty slim.

@Kevin Moules  not sure when you are coming to Phz if you want more info on things you see- connect with me and I can be available if you need anything.   

I do think it would be wise however to make sure you have credit lines available for future use If necessary.

Based on these objectives, the idea of paying down the mortgage while also having a HELOC available to invest is enticing. 

I will suggest this.... get in front of multiple lenders, ask for any grants that may be available, or other programs that might offer down payment assistance... usually for certain neighborhoods the city/county is trying to spur investment within. 

Inexpensive, fast, Good,  helpful, available education, close to you or is online fine, big, boutique, service etc.  

I do not know anything about your or its location but you might look into an apartment complex as a possible investment if any existing complex is available for purchase.