Duplex in LA - does the math look right?

[Mel Jones]

Hi all - welcome your advice
I'm a first time homebuyer with a husband and 2 young kids. We've been looking to find a duplex with two homes on a lot, and the environment is very competitive at this moment: at lower price points (625K max) only considering very nice streets in Hollywood/Northeast Los Angeles, with at least 1400sf for the owner unit and a decent lot (5000sf+). After losing a number of properties to all cash investors, we've gotten an offer accepted on a duplex- here's the stats

$615,000 (7,500 sf lot) 995sf front house, 2b/1ba, totally clean, enormous private deck with great views, rent could be 1800-2100

1500sf back house, also totally clean, 3bd/2ba, which was recently rented out as two separate units & converted back for sale, so the layout is as awkward as you'd expect two apartments fused together would be... but we think we could reconfigure and make it groovy. Rent could be 2100-2400.

We don't have 20% down to qualify for conventional, so we're looking at FHA with 5% down; Monthly payment will be about $4,200.

So, if our circumstances changed dramatically (we don't anticipate this,) we'd be able to basically cover the payment with the rents, though it wouldn't be positive cash flow right away.

Does this sound like a smart way into the market?
Our ultimate goal is to live in a normal house, and keep this as investment property indefinitely.