I greatly appreciate any help;

I just landed a much better paying job and I will start in couple of days. I've also saved up some money and I'd like to purchase a multi-family house near Los Angeles area (3 or 4 unit family house under 420K would be ideal).

I graduated from college on June 2014, I have some employment gaps in the past couple of years and they are as follow:

. Didn't work from 2011 to March 2014 due to attending college full time

. From June 2014 to now, there might be in total of 5 months of unemployment

I have an excellent credit score and I believe I can put down more than 3.5%. 

My question is: Do I still qualify for FHA or Conventional Loan or I need to wait? If so, how much more do I need to wait??

P.s, I'd like to thank anyone who can shed some light in here! Seriously thank you!!