This recipe is a good way to practice the Natural Minor scale, as as a rhythm exercise to work on playing in 3/4 time.
This progression can be described as either being in the key of A Major or F# minor. F#m is the relative minor of A Major.
When soling over this progression, you can use a F# Natural Minor Scale, which is the same thing as the A Major Scale, but just starting and ending on the 6th note (F#).
Use the arpeggios to learn the chord tones for each chord. The goal with arpeggios is to work parts of them into your playing over the corresponding chords, compared to running up and down the full arpeggio.
This progression can be described as either being in the key of A Major or F# minor. F#m is the relative minor of A Major. While playing an A Major scale would work well over this progression, it makes sense to think in terms of the F# Natural Minor Scale. If you play an A Major scale, but start and end with F#, you’re playing the F# natural minor scale (also known as the Aeolian Mode).