Yes you can choose a different host, you can keep your domain and just have it point to the new host and pay them to host your site.
I use bluehost, they can walk you through the process as they have a "live" help feature where you are chatting like this.
WordPress is the best in the world for creating a website, anybody tells you different---don't listen to em!
04 Chevy 3500
04 F350 Diesel
3 60" Toro Zmaster/Lesco 48"
3 8'2" Boss V-Plows
20' Enclosed trailer/16' Open trailer
18' Skid Loader Trailer
S185 Bobcat 2-Speed