Your sl 250 is enough, capacity wise, but not big enough flow wise. I would buy a second overflow boxand have it go directly to the sump, instead of thru the filter.
With the second overflow your pump could be an Iwaki 30rlt, Little Giant 4mdq, or a Gen X Mak4. I find these externals to be better than submersibles.
If you are skilled at pvc plumbing you can get a bigger pump and T it off to run the skimmer also. Remember to get a ball balve and a union to properly service the skimmer.
Skimmer wise, I would find one rated to app. 250 gal tank. I am old school, but I like the Berlin Classic with a Mag Drive 7, or tied in from the main pump.
Put a large powerhead in the tank to add in tank circulation.