Hi there,
You need a website for blogging, there are lots of option to choose. But as you said you are tight on budget, then I must suggest Google Blogger. Why? Because you don't need hosting for that. You just need to invest on a domain name and development. Once your website is settled (started earning or you have budget), you can move on to any other platform (wordpress etc), if you wish.
Regarding adsense, yes google blogger is fully comply with adsense terms and requirements. Off course your website design, responsiveness, mobile friendly, user friendly, On page seo, most importantly your website content, and few other things will also makes the difference.
And I can do all the these for you. Just let me know what kind of site design do you prefer. It will be great if you have any theme or website as a reference. If not, then i can show you some live demos of my work on Google Blogger, you can choose form them and I will modify the selected as per you needs.
Please reply so we can discuss. Feel free to discuss anything regarding this project before starting.
About Me:
My self Ajay KC, I'm a Freelancer Designer Developer and Google Blogger Expert. I'm in development of Google Blogger (Blogspot) from past 7-8 years. I have a good knowledge & an extensive experience of Blogger Blogs. I can create, edit, modify any blogger blog/template/design (css-html-javascript). I can show you my live work Samples, if you need.
Looking forward to hear from you.
Thanks