You can have blog on your site, create a new site for just your blog or create blogs on existing blog sites. All approaches work and if you are into tiered link building you may employ all three tactics to create links and traffic for your site.
Web tools: Yes, it would certainly help if you have a blog on your own site, for one you can get to know what people think of you site, additionally your web site visitors will have a way to interact with you.
Yes, its a good idea to start with a blog for your Website. It can help you get people know about your website, additionally if your blog contains quality and unique content, Search Engines crawlers will visit continuously, if you post on regular intervals, which will help you to get enough traffic too.
I think the only way to go is have your own, hosted blog. It will give you the flexibility to change the structure, look & feel etc etc as well as the all important – ‘who owns the data’. You don’t want to end up in a legal wrangle if your blogging platform goes down & you have no recourse.
Yes! since there are a lot of web tools that can help you with setting up a blog, it would be a great idea if you can have a blog of your own on your own web site for one you can post current updates additionally you will be able to keep a line open wherein you can interact with your visitors and if they have any adverse comments regarding your site it sure will help in taking their opinion into consideration in-order to enhance your website further.