You will be able to run some of the Games on a standard A1200, it's not the speed that is the issue it's the amount of ram needed to load up the game, from floppy disks this isn't an issue but whdload needs some extra resources.
The A1200 you linked is fine but you will need a trapdoor ram upgrade, 4mb is sufficient for most Games, 8mb is better (helps to pre-load larger games) and an accelerator with 16mb+ is optimal.
You can fine them used on eBay and Amibay and Amigakit/Vesalia stock the new ACA range of cards:
As a guide, Fast Ram cards will cost between £40-£60, the ACA Cards you can find the prices on Amigakit/Vesalia's sites.
Budget accelerators tend to fetch £70+ and the Blizzards £130-£150, you'll find some eBay sellers chancing theirs at £200+ but they wont sell.