Seems that you are trying to do lots of new things at the same time, I suggest that you break your task down into small steps, this will help you learn the new concepts, and new tools.
Steps I would try:
A) Get your domain name to point to your new hosting, your hosting providor will be tell you what DNS settings to put into your settinsg at Domain.com. This can take some time to become effective.
B) Can you login to your hosting management ? When you can you can find the settings you need for filezilla.
C) Create a file callsed cats.html with these contents:
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
<meta http-equiv="content-type" content="text/html; charset=utf-8">
My test webpage.
Then connect to your site with filezilla and upload thsi file.
You should then be able to view this file.
Then install wordpress, get it going with the default theme.
THEN install your chosen theme.
Keep notes of what works etc, and report progress here.