Absolutely get your domain and hosting in your own name so you retain control. Some good advice on the DO NOT's here.
If you want a list of programs you can use that are free as opposed to buying Dreamweaver and PS to help make your website let me know. I also have a wide array of resources that I can send you that may help you with design and code. I might make a section on my website with some of these resources for ladies who have the time or desire to do it themselves if I can find time to update my own website.
Best of luck to you creating your website. Have fun. Let us know when you get it done.
Thanks for the plug Reese