Upgrading iPhoto from OS X 10.9.5 (for High Sierra update)

Hello all! This is my first question on this site, and I am a bit confused about some steps I'm taking towards upgrading my OS. I apologize in advance for this long post, as I want to explain my question as clearly as possible!!

I have a 5 yr old Macbook Pro Retina (13'') currently running on OS X Mavericks (I know, I know...totally behind! I'm afraid of change!), and I received encouragement to upgrade after a recent battery replacement. I am hoping to update to at least OS X High Sierra, as it's the one the App Store is recommending to me. To add a bit more context, I am looking into purchasing a graphic art tablet that only runs on OS X 10.11 or higher, so this also motivates me to update.

However, here is my main issue: I noticed that there are many app updates in the App Store that are "incompatible", and I have downloaded the most recent versions compatible before the High Sierra update. I am aware that iPhoto updates were dropped by OS X Yosemite's release unless you upgraded to 9.x. Luckily, I can view it in my "Purchased" tab next to an "Install" button, but how can I proceed from here?

I've heard you can update through an uninstall, reinstall process, but also that you can switch to "Photos". More than anything, I just want to make sure my photos are safe, and everything will be compatible with OS X High Sierra. I would appreciate any advice in helping this process run smoothly! Thank you so much!

-Céline