You can significantly mitigate the costs of marketing your blog with some careful (ethical) SEO (search engine optimisation) tactics.
Primary among these is to have a blog which is web standards compliant. Search engines love standards compliance – to this end, WordPress is a great blogging tool as it is standards complaint out-of-the-box. Having said that, if you have access to a developer, you can get the developer to design a standards compliant template for most blog apps.
Secondly, generate inward traffic/links. The only way to do this (apart from paid ads etc.) is to generate content on your blog that is compelling enough that people will link to it. Also leaving relevant comments on other’s people’s blogs will bring curious readers of those comments to your site.
All these take time and effort but they will ultimately pay off and are free!