You need to create WordPress Post Gallery to set any Gallery in the Front Page. WordPress Gallery Creation is so easy and it is just like a New Post Creation. This Tutorial may help you on creating Gallery.
You can create multiple Gallery Posts. The Posts’ title will be the Gallery title. Normally the latest gallery post is displayed in the front page. But you can set any post’s ID in the NewsPress Options to show any specific gallery post.
You should also create a page and set the Page Template to All Gallery. You can use the link of that page to show your all galleries in one place. You can also set the Link to any Specific Category to better performance.