Transfer a Wordpress Site to a new domain name

Hello, We need to transfer our website from [login to view URL] to sh8pexplore.com. I have already installed wordpress on the new hosting account (xplore) and have created FTP accounts on both websites. I will provide all the login details to you and this should be simple with a good internet connection. The problem for me is that I am travelling and don't have sufficient internet to complete the task. It is crucial that you have done this before and understand everything that needs to be done inorded to change every link within the new site to the new URL etc so that there are no broken links etc. But this should be a simple Filezilla type process simply copying and pasting before editing PHP etc. I have done this before and am familiar with the process but this is going back 2 years. The budget is modest as the request is also. Thank you, I am looking for someone reliable to assist me from time to time with things like this. I expect this to be completed within 24 hours.