A Banded Planet
In addition to what StephenG and kingledion said, you don't mention a moon, which is very important to the movement of our oceans and interaction with land. Frozen poles? Jury is out on that with either no ice or significantly more. Scholarly articles get tough to decipher but a friendly person on reddit has helped (link) and included links to studies. The jet stream bands may largely cut off heat transfer north and south resulting in larger ice poles. Other models say smoother deep water exchange would shrink the polar ice or eliminate it though it may be perpetually snowing.
What aquaplanet modeling studies have in common is that the jet streams would be straighter without mountains in the way. This would follow for all winds and pretty much weather as well in that it would all be based on latitude. On our earth, warm ocean currents keep Europe warm while similar latitude Canada is colder. Not on your planet. So pictures of Jupiter might very well show a pattern you're more likely to see.
Ocean currents might follow suit but they are a bit crazier, also dependent on ocean floor topology, here is a link to NASA animation of our currents, look right toward the end where it's just the Pacific looking like your aquaworld, overall get some bands but lots of gyres and swirls.
Rainfall may depend on ocean depth and uniformity and which model you go with (polar ice or not). Overall my hunch is that it would be similar or less but once again intensity would be relegated to certain latitudes.