It used to be the case that you could either choose to have a site hosted for free, and have it full of adverts that you wouldn't get paid for, and have no control over the domain, or you could pay for a premium service to have full customization.
Thankfully, the Internet has come a long way since then and you no longer need to choose between those two extremes.
You will be happy to hear that you can now have you site hosted for free, design it to look EXACTLY how you want it, and even earn money from it (if you wish), without having to spend a penny.
When choosing your platform, you should consider what you want your website to be for, is it going to be just a blog? Will it sell something? Is it just for information? Will it have advertising? Once you have the answers to these questions, you will be able to determine what level of customization you will need.
You will also want to consider the content of your site, will it be text based, will there be a photo gallery, will you want to embed videos into it, will you need a members area, all of these questions will also help you decide the level of support and customization that you will require.
Don't worry though, you won't have to learn any code or expert design techniques, there are some very good platforms out there that offer an array of support and freedom to design.
Sites such as WordPress or blogger have decent designing facilities and a basic level of customization available for amateurs, as well as a relatively nice amount of help and support.
In my opinion though, it is not worth taking the time to learn these platforms when there are better ones out there, also for free, with a much higher level of training available.
If you could have your own free account in a website building training center, with access to two free websites of your choosing, along with complete training videos, blogs, tutorials, and live chat to help you get the site set up, wouldn't it be better than signing up with another "free" platform and having to use Google and trial and error to learn by yourself?