Okay - first things first, you have to think of the contour. Is it white note to white note; black note to white note or white note to black note (physically black note to black note is the same as white note to white note as the keys are again level in height, despite black keys being thinner).
I would literally take just the first 7 bars of Hanons Virtuoso Pianist and play it slowly, but heavily (not forced) but just deliberately played. I would play it as it (in C Major), then as an exercise I would play the same exercise in a 'long-short' manner (think like a dotted quaver-semiquaver manner where the first note of each pair is held 3 times as long as the second note in each pair; as opposed to straight quavers), then the same in a 'short-long' manner (think like a semiquaver-dotted quaver manner where the second note of each pair is held 3 times as long as the first note in each pair; as opposed to straight quavers)
Then I'd do the same thing but change only the E's to E flats, and as a 2nd challenge, do the same thing but change only the F's to F sharps.
Again... SLOWLY, loudly (not forced) but deliberately and in a manner where you don't feel any fatigue. You will find trills with all manner or fingerings, so it would be good to get used to both. I think the 1-3 is a little less common though compared to the 2-3.