A MacBook Air (13-inch, Early 2014) can run Catalina, or even Big Sur.
Catalina isn't one of the "most recent three" major versions of macOS any more – while Big Sur is, if only for a very short time – so you might upgrade to Catalina only to find that it wasn't enough to let you run current applications from, say, Microsoft and Adobe.
Big Sur will run on a Mac with 4 GB of RAM, but you might find that amount constraining. According to Apple's technical specifications, if you are upgrading from High Sierra, you will need at least 35.5 GB of free storage to install the upgrade. Note that neither Catalina or Big Sur will run 32-bit applications. You may want to check if there are any of those that you will need to upgrade or replace before installing the upgrade.
macOS Big Sur - Technical Specifications
The App Store normally hides old versions of macOS, so to upgrade, go here:
How to download and install macOS - Apple Support