You can pretty much pick a blogging platform and run with it. WordPress, Blogger, whatever–just try out different platforms and see which ones you like better. The biggest thing is to make sure they have a feature that will let you export all your posts so if you ever do decide to move you can take your content with you easily.
To get readers, you can absolutely post on FB groups to announce your new blog (if relevant and allowed) but be careful about doing something like posting every time you write a new blog post. That sort of self promotion can annoy potential readers who would be subscribed to your blog if they wanted to know about every new post.
You should also add your blog link to your signature and/or profile for any social media platforms you are on. It makes it easy for people to find you, especially if they like what you are posting on those platforms and want to see what else you write, but isn’t as overt as “I wrote a new blog post! Come read it!”
But when I was blogging regularly, I found the best way to get readers was to be one–I’d read and comment on blogs I liked, and often the bloggers and some of their readers would stop back by my blog. Some would start reading mine regularly. You become part of the community that way. I wasn’t the best at doing it, but there were dramatic differences in the statistics when I was actively reading and commenting and when I was just passively writing and letting people find me.
Don’t get too angsty about things like tagging your posts and thinking that will help your search engine rankings. Especially while you’re a new blog with zero internet authority… they really won’t. Write good content, use tags that will help you and your readers find relevant posts on your site, and the search engine rankings will come. With some very rare exceptions, you’re not going to get new readers from random internet keyword searches.
You will need to do some sort of promotion so people can find your blog, so just figure out what you are comfortable with and how much you want to do. And then, yes, start a blog and just start writing. Write frequently, write thoughtfully, and write authentically. Have fun!