Or do I  open any saving account with all 3 units ?

Live in it for one year then save up and purchase a second property somehow. 

I have about 100 Grand in equity in my first property and about 70k saved in cash.Any advice? 

Then, weigh the options: sticking with the current rent ensures ongoing income but might risk tenant dissatisfaction, while offering a reduction can incentivize renewal and save on vacancy costs.

Save your texts and such with your tenant and your calls to the police— build a record of your neighbor’s noise.

But here's where it gets truly electrifying: our savvy client is seizing the reins on a remarkable 10-year tax abatement, already one year in, opening the door to a decade of substantial savings.

If you don’t want to leverage your house then you need to save more cash.  

Our goal is to purchase our first multi-family in Brooklyn or Queens and move in once our lease is up.Background- Both work remotely- No debt / No Kids- $250k+ in savings for a downpayment (should we do an HFA?)

The extra income from the extra units might allow you to do more than break even in saving some of the cash flow you would usually have to put out. 

I always prefer working with referrals over someone I've found online etc.