Welcome aboard
What is the best solution for playing my favourite old games?
Do all the games come in all the formats? Ie if I buy some form of 1541 emulator will I still be able to play all my old favourites or should I get a Datasette Emulator instead or do I need to go down both routes?
Well... roughly speaking, images of C64 programs (specifically games) come in two flavors: images taken from disks are usually in form of files with .d64 extension; instead, images taken from tapes are usually in form of files with .tap extension.
That said, if you want to be 100% sure to be able to play your old games, you have basically two options.
If you still have your old games on their original supports and these are still working, you can of course load them by using the physical machine and its own peripherals (if you don't have them or they are not working anymore, you can buy them for cheap prices on the major sites of e-commerce). If they don't, you still need the peripherals in order to take working images from the Internet and transfer them to the physical supports (there are plenty of references on the Internet explaining the process in depth).
Otherwise, you can use a software emulator of your old C64 setup and load the images of your old games from there. To my knowledge, the very best ones emulators are freely downloadable from the Internet and they are VICE, CCS64 and Hoxs64.
Cheers