If you bookmark your favorite sites in the Favorites folder, then they will show up on those blank pages with that the + icon invokes. They can be re-ordered by using the bookmark icon, navigating to the Favorites folder, and tapping Edit at the bottom of the list.
The red circle lets you delete an unwanted bookmark. The lines icon at the right lets your drag them into whatever order you like.
As you see from my example here, it's actually possible to create folders here, for extra organization.
The Favorites that show up when you create a new page can be set to any folder under Settings > Safari > Favorites; but it's usually best to leave it set to the actual Favorites folder, to avoid confusion.
If you turn on Show Favorites Bar in Settings > Safari, you'll also get the list of favorite links just below the tool bar (as in my screenshot). If you have folders, as I do, then those links become menus. You tap on them to see a list of links.
The Favorites Bar is always the Favorites folder, regardless of what you set in Settings > Safari > Favorites. This can be handy if you wanted two sets of favorites, on in the Favorites Bar for the most common stuff, and one that shows up when you create a new tab.
Safari's bookmarks are surprisingly flexible, but of course that also makes them a bit harder to get used to.
The Favorites Bar is my usual method for keeping favorite sites bookmarked. It's organized and fast.