Hi Ziq, don't worry about your English...I think it's better than mine!
Public transportation in Malaga is usually pretty safe and reliable, whether you're using a train or, more likely, a bus.
As for where to stay, it might be tough to find places, but check
this place out. It's near the beach and seems to be within your price range. I haven't stayed at this specific property but I have stayed at one of its sister properties and was happy with the service/value.
Good luck!