Sure, here is a simple drum pattern following your guidelines:
BPM: 120
1. Kick drum on beat 1
2. Snare drum on beat 3
3. Hi-hat playing 8th notes (constant rhythm)
4. Adding a shaker sound on off-beats (e.g. 16th notes) for more texture and interest
Here is a visual representation of the drum pattern:
1 + 2 + 3 + 4 +
K x S
H x x x x x x
S x x
(K = Kick drum, S = Snare drum, H = Hi-hat, x = shaker sound)
This pattern should create a nice groove with a bit of movement and variation in the rhythm.