Self Hosting

You'll need a domain name, and a hosting provider to begin with. My word is to go with the branded, though it is little costly, but trust is retained. I have had many experiences in the past, and after that there are only very few hosting providers I could trust upon. Personally, all my blogs are self hosted (though not regular) from years, so I can be an experienced grandpa at this :D I have been taking my doamins from bigrock and hosting on hostgator. These are simply, THE BEST. but that's my view.

Hosting is of different types, skipping the details, you need a shared web hosting, nothing more will be needed unless you plan to take a big hit of about more than a million views per week. 

Next comes a blogging platform, best would be going for Wordpress. it just does the magic, and is much user friendly. Oh and yes, you need a 301 redirect on your existing blog to ensure the search engines know your blog has permanently moved to a new address, and the older link juice and SEO benefits are duly retained and passed :)

You can find plenty of How to's on the interweb, and can always contact me if you need any discount coupons or further guidance. Cheers!

PB