If you want to keep your stock rim,the hub will need the same number of spokes. Wheel size only matters when it comes to getting the proper length spokes. You will probably need new spokes,and it's very likely you'll need new nipples as well. Cost varies,but a good ballpark would be $1.25 a spoke and $.50 a nipple. Build cost will depend on the shop;costs are higher in certain areas,and some shops are more high-end than others. If you don't change the size of the rear cog,you don't need to do anything with the chain,but the first gear is direct drive with the second a higher gear,so if you're looking to gear down for hills you'll want to put on a larger than stock cog. Whether you need a new chain or can just add links will depend on how much room you have to move in the dropouts and if your chain can swap links(many newer chains have shouldered pins that can't just be pushed in and out).

Also note,folks have had to disassemble this hub and play with the shifting spring to get the shift point right for a small wheeled bike. Just something else to consider.