Ship Model Base

Depends how fancy you want to get. I have used a piece of 1x4 or 6, with screen molding glued around the edges. Stained, it looks just fine to me. If you want to get fancy, painted plaster or clear resin over paint can look good on a waterline model.

Go to your local Lowes or Home Depot with the model's measurements.   You should be able to find a piece of wood which will work for you.   Lowes & Home Depot also offer cutting services to cut the board to length.   While there pick up a pack of assorted grit sandpaper and a rattlecan of clear varnish (they make an acrylic low odor version).  If you go with oak you won't need stain. 

Sand over the edges of the board to round them.  Coarse grit to fine.  Wipe off the board with a damp (not wet) paper towel to remove the dust.   Lay on a light coat of clear, let it dry, sand smooth.   Repeat.  Three or four coats of varnish will bring out the shine & beauty of the wood.

If you are modeling in an apartment this process is similar to the dust & fumes raised applying and sanding putty.   If it gets bad -- spray the paint in the laundry room.

I would say a 1x8 from home depot. It will be 7-1/2 inches wide, they can cut it to length, and if you still have your router it can be done in an apartment. Sand it outside anyway.

 You certainly could finish it in an apartment.