The theme is the design of your website. It is essential to have a theme which you feel comfortable with, which makes you feel like writing posts. The first theme you will select is probably not the last one you will try. I’ll recommend you to start with a free theme you like before moving to a paid version you could get on http://themeforest.net for example. It will allow you to identify which features are really important to you to select later one a more appropriate one.
To update your current (default) theme by a new free one, go on Appearance and select Themes.
Once you there, you can see the current theme available on your account. The first one on the left-hand side is the active one.
To add a new theme, click on Add New.
At this stage, you can filter, navigate to find the one which is the most appropriate.
The Upload Theme button would only be for Theme you would have bought and need to upload.
When you put the mouse, on a given theme, you see in the middle of the picture Details & Preview and below the picture Install.
Once you are ok with the theme, click on Install.
Once you see the following screen, click on Activate.
The new theme is now available. It appears at first on the top left-hand side corner.
Here is the website before and after: