Yes, you can use Wordpress. Many people here are using WordPress. Even our Kayla uses Wordpress for her blog. To install it, you only have to go through Cpanel, and with a few mouseclicks, voilla, you will have a weblog
Regarding your other question, as far as I know your site should either be HTML or PHP, not sure if ASP is working.
Also I believe that with the cheapest package you will have enough space to create your personal website. Word of warning though, making websites can be enslaving.