Hello everyone. I am looking for the apartments in LA but feel it is so confused about this city. I am living San Francisco now and love here! However have to move to LA next month becuase of the job. I find that LA is totally different then SF, it is a HUGE city!!!

I have no idea that which area is safe and cozy for the new home. It will be much appreciated if you could give me any advise.
I am looking for the apartment:
1. Safe!!!!!!!! Good neighbourhood!!!!
2. Convenient transportation. My job is in San Ta Fe Spring
3. Conveneint for grocery shopping. That will be great if have cofe, nice restaurants in the neighbourhood.
4. Budget is under 1600 for 1 bed/1 bath.
If you could advise on below that will be much helpful!
1. Which area is good choice for me?
2. Any good way to find the apartment in LA? Angent? Craglist? Or any others?
3. Any good apartment could recommend?
........
I feel so worried about the new home now, and your help will be so grateful!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!