For the Browse menu specifically, you can reorder this via the user interface, using the Menu module at Admin > Menus. Find the browse menu parent node - you will see up and down arrows next to every child node in that menu. Clicking the up arrow will move the selected menu item up in the order:
If you want to change the labels that appear in the browse menu, click on one of the menu nodes, and in the edit screen, change the value of the Label:
For more significant theme changes, such as changes to colors, and/or page layout: the best way to make changes without preventing you from upgrading in the future and losing all your changes is to develop a custom theme plugin, and use template overrides in the theme to make your changes. The following post in the forum has a good overview of how theme plugins are organized, as well as some links to other theming resources we have:
I'm also attaching a PDF that covers much of the same information on how a theme plugin is organized, and how to install a custom theme in your local installation.
You can also see every post that has been tagged with "themes" in the user forum in the last several years here:
Cheers,