Slow move

I have begun taking my slow, faltering steps towards transferring this website, and my personal site, to a different host, having become fed up of the last one. The new is considerably more expensive, but reputedly reliable. I am rather nervous about this whole transferring business; I’m not as savvy as I pretend to be, and don’t find the guides online particularly clear – nor does the new host use cpanel which is tedious but familiar in a Windows 3.1 sort of way.