How should I connect these beams to the posts?
If you want to avoid the steel braces and have an attractive, complete wood look that is also strong, there are a few ways. A combination of strongbacks on the outside faces of the posts and cornice braces from the post to under the beams would look great and stabilize the beams.

The strongbacks are short 2X4 pieces, perhaps champhered, top and bottom,  that would screw into the post and also the beam on the outside parameter. Two are required for each post. The beams should be cut at 45 degree miter angles or notched to fit together and lay on top of the posts.  The cornice braces typically are triangles or 45 degree braces that mount to the sides of the posts and the bottom of the beams. Again, two per post are required. You can then screw some timber ties or long lags down through the beams from the top into the posts.

you can fancy up the cuts on the strongbacks and braces to enhance the style.  The combination of beams sitting on top of the posts with side and bottom support is extremely strong.