Since you are going to host a blog, take note that it may be resource intensive.
As such, you have to read the TOS of all the host that you are considering to check their limits on cpu and ram resource usage as most host tends to limit you that way.
Your budget is quite ok. Remember that your host needs to allow you to have add-on domains as well.
I think that with your budget you can find a decent hosting provider that will provide you with a lot of space and bandwidth so that your website can have all the room to grow in as your content and visitors increase. Regarding CPU and RAM usage, most web hosting providers allow you to use 5-15% of their shared resources for 2-3 seconds or not more than 10% at a time. It will be enough for your start up website and if you have the luck to have a website that will go over these limits this means that it will have become very popular and probably you will have the resources to think of a better solution like a VPS or dedicated server.
You can prob start on most starter packages that hosts here offer you. Once you start growing larger, just upgrade the accounts accordingly.
If you visit the offers section, you'll find pretty good deals. Try to find a company you like and research it. A little research here will help you from the headaches later down the line when your hosts just disappears.