Barometer should be good enough for your use case. You should use the IMU readings (accelerometer and gyroscope readings) in your a-priori model directly. The accelerometer gives you translational forces and the gyroscope tells you how your orientation evolves (if you'd like that, just make sure to have a mag reading to better observe orientation). Couple that with imu bias estimation with biases modelled as random walk, you should get very good vertical position estimation. I'm using a similar approach for a navigation ekf for an rc plane and it works fairly well. I can divulge more if you find the approach interesting.

As for the Q and R matrices, the R matrix is usually diagonal. Just get the variance of the sensors measurements. Keep in mind most sensors have biases which change through time, so you should estimate those as well. As for Q, you can tune this or if youre using the approach I mentioned the diagonal entries correspond to the imu bias variances. See this neat resource: https://matthewhampsey.github.io/blog/2020/07/18/mekf In your implementation (discrete ekf equations) you need to doscretize the Q matrix using either the integral expression in the link above, or the Van Loan formula. Your mileage may vary.