Back up

Literally any external USB hard disk drive will work.

Speed is not particularly important. Buy one with sufficient capacity to contain at least twice the amount of data you're using. Considering the maximum capacity of a 2014 MBA was about half a terabyte, a 1 TB drive is sufficient. Twice that amount isn't much more expensive.

Depends on the size of your internal drive and the backup method. If you’ll use Time Machine, best to have capacity of 2-2.5x the amount of data. If you’ll use a cloning utility (SuperDuper! or Carbon Copy Cloner), you only need something the size of your internal drive.

USB thumb drives are inexpensive up to 256 GB, and you can get one (e.g. SanDisk) with both USB-A for your Mac and USB-C for if/when you get a new Mac. If you need >256 GB, a 1-2 TB USB 3.0 HDD is the way to go, <$100.

I recommend the Mercury Elite Pro drives from OWC (macsales.com). They come in many different sizes and different flavors (SSD or 7200 rpm spinning hard drive). Good quality and dependable. And, an SSD is very fast, but really not necessary for a backup drive - 7200 rpm drive wil be fine and far less expensive.

Remember one thing: no matter which drive you decide on, no external drive needs any type of software on it to function, so when I get one, plug it in, launch Disk Utility (Applications folder > Utilities) and format the drive for Mac. The process will erase anything on the drive (which is fine). Then you are ready to back up - either with Time Machine or a clone.