Google Analytics is a way to keep track of how your Web site is being searched for and accessed. Information about where the users are located, what devices they're using, what pages they're interacting with and how they find your Web site is included. You'll get a feel if that Facebook Ad you placed brought any new traffic to your Web site. You'll see that the new post you wrote is really getting a lot of hits.
You'll probably want one or more email accounts associated with your new Web site. Examples would be YourName@YourDomainName.com and Info@YourDomainName.com and Reservations@YourDomainName.com
To save effort on setting up your new Web site, you can embed items that you already have on your Houfy listing. When editing your Houfy listing, you can find some items have an "embed" button. When selecting the "embed" button, Houfy will display the HTML necessary to integrate into your Web site.
What is WordPress?
I've used both Hostgator and SiteGround. I don't have personal experience with GoDaddy, but I can say that I haven't heard many good things about them.
Your domain name will be the URL that you use to direct users to learn about your property and to have them book with you. The domain name should be shorter, somewhat unique and easy to share. Preferably, you can create a brand name associated with your property or vacation rental business ensuring these 3 traits.