With so many great guides and how-tos to the blogging game I've been a bit hesitant whether I have anything of value to contribute to the topic. Especially because my blog is still new to the sphere and currently still under the development. However, I feel like I've been doing this for long enough time to be able to add my own two cents.
Assuming you already know what you're planning on blogging about choosing a platform would the next step. I originally started with wordpress.com and had been on it for a couple of months before I decided to level up. During that time I tried out dozens of templates, changed my layout a good number of times. I think it's a good time to play with the themes, try different settings and see what suits you best before you take the next step. I was never fully happy with the platform, hence the reason I moved to a different one.
Personally I love a good header. I've always been very particular about mine, I know what I like and it took me ages to find the right person to do it for me. It can be pricey sometimes but I think it's worth it as not only does it make you stand out but also it looks way more professional. Once you know what you're after it's good to do a bit of a research online. There is a number of places you can purchase one from. Etsy offers lots of options, Jemma from Dorkface does cute headers or you could search for local artists. I've been following Annie on twitter for a long time before I build up the courage to email her asking if she could design a logo for my blog. Best decision ever made because now I can't stop looking at it. What you could also do is to design your own one in Photoshop, Picmonkey or any other software. I used to purchase lots of cute fonts from the Creative Market (or get the weekly free ones) and play around with the Clipping Mask tool in Photoshop. Here's the tutorial I used.
Once you're happy with the name you could consider buying your own domain. It's not expensive at all and it definitely will make your site look more professional. I bought mine fairly early and paid about a tenner for it. I thought that was the next reasonable step to make.
Changing a platform can be an option. I decided to transfer mine mainly because I thought my previous one was too restrictive and not allowing much choice and options. I originally went self hosting thinking that is what I should be doing, probably because everyone else is doing it. The problem is everbody makes it always look simple, easy and fast. It was none of those from my experience. I'm not the greenest when it comes to technology and internet, I would like to think I know what I'm doing most of the time. For some reason though I found self hosting too much and cancelled it within a day. I've researched a lot instead and decided SquareSpace seems much more user friendly. The domain and the content migration did cause a bit of a trouble but all ended well. Their support is great and so far I'm a 100% happy with it.
Right now I'm still changing bits and bobs. I think I'll be like this forever since I find it extremely hard to settle for one thing only. I'd advise you do the same, you never know what you might like. I'm still really bad for consistent posting. It's the main thing I'm dying to improve. I spend a lot of time on photos taking. Mainly because I'm incredibly fussy about visual aspects, I'll be forever working on one picture until I'm fully happy.
I shout about mine on Twitter and occasionally on Instagram. Lots of bloggers offer paid advertising which can be great for bringing more traffic to your site. Depending on your content you can try searching for bloggers with similar ones you could advertise with. I've not tried it myself but I might be considering it in the future.