you do not freehand on a router table, my friend.
Make thee a smooth shape in 1/2" plywood as a template, trace the shape onto your piece of wood, then jigsaw or bandsaw close to the line. Then, use pin nails or screws to attach your template to the workpiece on the B-side (the side that is not seen) and cut it with a Bottom bearing router bit
Repeat for every piece.
MDF doesn't have a lot of grain pattern, but it will soak up a bit more finish on the cut ends than on the faces.
The steps I follow to finish MDF seamlessly has always been to flush-trim the edges with a bearing flush trim bit, followed by sanding to 220 and primer before final finish. The trim bit (if you have a router) saves a lot of time sanding.
This is the flush trim bit I use: https://www.amazon.com/Dia-Bearing-Flush-Trim-Bit/dp/B0000225YC/ref=sr_1_2?ie=UTF8&qid=1464796548&sr=8-2
Use a circle jig to router out a 10" out of some scrap wood, clamp that to the mdf, then use something like this to cut the bigger circle onto the mdf.