Which rudiments should you learn first?
Learn a few sticking patterns well enough to use them in time.
Rudiments give names to useful hand patterns. They can help with control, accents and moving between drums, but memorizing the list does not teach a song arrangement. Start with a few patterns and hear how each behaves at a manageable tempo.
Singles, doubles and a paradiddle
R and L mean right and left hand. Single strokes alternate: R L R L. Double strokes use pairs: R R L L. A single paradiddle is R L R R L R L L. Say an even count and give each letter one note.
Begin slowly enough to play two clear strokes with one hand without squeezing the stick. In the doubles and paradiddle, listen especially to the second note of each pair. It should not disappear or arrive early. Increase the tempo only while the spacing and sound remain controlled.
Hear the flam as one figure
A flam has a quieter grace note just before the main note. Start with one hand close to the drum and the other higher, then strike so the lower hand arrives just before the main stroke. Reverse the hands and compare the sound. It should be a close two-note figure, rather than two equally loud notes spread across the beat.
Use one pattern on the kit
For a 4/4 practice example, play three bars of groove. In bar 4, keep the groove through beat 2, then play R L R R L R L L as sixteenths across beats 3 and 4: "3 e & a 4 e & a." Start on the snare and return to the groove on the next 1.
Once the return is steady, move only the first note of each four-note group to a tom. If moving around the kit changes the spacing, go back to the snare. The goal is a pattern you can place in time, not a faster sticking you cannot return from.