Which program from the Adobe branch should I choose?

Honestly, you'll find plenty of animated GIF generators online which are more practical for this than Photoshop.

Adobe has an entire range of products and services for various types of designers.

• For UI/UX, look at Adobe XD (experience design).
• For pro -level image editing, Photoshop CC can't be beat but there's a steep learning curve. 
• For hobbyists & amateurs, Photoshop Elements is a simpler and more affordable option without all the fancy bells & whistles. No subscription required.

The Creative Cloud Photography Plan is a deeply discounted bundle of products & services for approx $10/month.  A 1 year commitment is required.
-- Photoshop CC and Photoshop on iPad
-- Lightroom on desktop, mobile and the web
-- Lightroom Classic
-- Portfolio website + hosting
-- Spark with premium features
-- Bridge
-- 20 GB cloud storage (upgradable to 1 TB).

Creative Cloud All Apps (31 + desktop/mobile apps & services)

For someone needing more than 3 Creative Cloud products (XD, Photoshop, Illustrator, Acrobat), this would be the best plan option.

Please ensure your computer meets or exceeds the minimum system requirements to run Creative Cloud + all other apps you intend to use. Check each one carefully.
https://helpx.adobe.com/creative-cloud/system-requirements.html

there are several programs that could be used to create animated gifs, but photoshop would probably be the best app to pick because

1.  it's the industry standard for bitmap creation and editing

2.  it will create animated gifs

3.  the photography plan (which includes photoshope and lightroom) is the least expensive plan