Whatever you do, do not move to 000webhosts paid service. Ask them for your data base and your back up. Pretty much shure you can download both from 000webhost without asking them. First make sure your back up is up to date before downloading.
Next find a good paid host, before you sign up ask them if they will transfer your site for you. 99% of good hosts will do this for free. Simple as that.
If you are having problems, look for video tutorials on Youtube, it makes it far more easy watching the process in action.