Welcome!
There are many ways and all lead to Rome.....
The Sharpmaker is really hard to beat especially if you have limited experience, and no experience in freehanding. You can upgrade for $16 to the UF stones and get even more polished which will make an even better push cutter.
A strop with some compound is always a good idea, not only does it polish up an edge, it takes care of most residual burrs and you get a good edge quickly an easily. The strop should be backed to minimize rounding over the edge (which will happen but on a backed strop only to a small degree).
You can also buy very fine "sandpaper", or rather PSA backed abrasive sheets that go down to approximately 0.5 microns which is about the same as the compound commonly used for stropping.
In my opinion the last word in polished edges are waterstones, simply as there are finer grits available than in any other medium and you can grade them finer using a Nagura and by building a slurry. However, if you get creative with strops you can find some pretty amazing compounds aswell. Usually waterstones require you to learn how to freehand but you can use jigs like the one from Razoredge and the Edgepro has waterstones available as well.
Really, the answer is: What ever works for you. I find, that the better (more experienced) I get, the easier it is for me to do with less than perfect equipment. On a blade with a good geometry and an edge that is not too far gone you can even get easily shaving with the bottom of a mug.
Maybe to put things into perspective, Benchmade isn't even exactly famous for their factory edges. I don't say that to dampen you enthusiasm for them but simply to say that you shouldn't aim for factory sharpness but that you can, with practice, beat a factory edge. However, cutting ability is not only depending on how well you sharpen, but also on what kind of geometries you are employing and you might not wish to go to significant smaller angles than the one used by the factory as it puts a larger (and by many viewed as ugly) bevel on the blade.