Do you want a QR or bolt type clamp?
I use hope clamps on most of my bikes. They have aluminium bolts so you really can’t overtighten them (or they snap) but I have never had a problem and it’s nice to have a ‘fuse’ in there.
I also have a Thomson bolt up clamp which is lovely.
But tbh I have never had a problem with cheap clamps that came with bikes. The faces meeting does sound odd. But check your warranty as some makes can be funny about changing things like this.
Salsa make very nice QR clamps.
And yes, use carbon paste but first de-grease the tube and post with something like IPA as the manufacturer will probably have used some grease to prevent corrosion.
also there should not be much play with the clamp undone. If there is a lot then it suggests the post is undersized or tube oversized and I would be going back to the shop to get it checked.
For size – you still need to check the actual diameter of the seat tube in the frame. 31.8mm is the most likely though with 29.8/30mm being common for steel.