Tape games were more popular in the UK, due to shops selling them more than disks. However in some countries (esp the USA), disk games were the main format. A lot of the strategy games from the likes of SSI used this medium to the maximum.
Cartridge games were produced both at the C64 inception (mostly by Commodore, Parker Bros and a few other companies) and also when Commodore launched the C64GS (basically a 'console' style version of the C64). Ocean, Microprose, Gremlin and US Gold supported the cartridges and produced a few good games. You should be able to get hold of some cartridges on eBay (along with tapes and disks).