CF cards are getting very hard to find in shops these days, you would be better off with a PCMCIA Multi-Card adapter or SD Card adapter, and use cheap SD cards. But as the others suggested, using a card reader in the PCMCIA slot is definitely the best way to transfer thousands of ADF/DMS files to real floppies through your A600.
The problem of course is getting the drivers onto your Amiga in the first place. If you're willing to trust someone on the forum with your address, perhaps they could send you an Amiga floppy with all the necessary software (card reader driver, FAT filesystem handler and ADF/DMS transfer software) and you could easily buy a PCMCIA card reader online. I use this model -
http://www.dealextreme.com/details.dx/sku.23720 but you can sometimes find them even cheaper if you shop around.
You really should also install a new internal IDE drive. By far the best option for A600s is to get a Compact Flash or SD Card adapter for the IDE port and use a 2-4GB card with two partitions on it. Then you'll be able to install Workbench and WHDLoad, allowing you to install thousands of games on the drive instead of having to write them all to floppies. You can get these adapters here
http://www.dealextreme.com/details.dx/sku.10310 (they have SD ones too but they cost more, so if you can find yourself a CF card you're set).
You might also want to upgrade to Kickstart 3.1 because 2.x is kinda useless these days, 3.1 barely uses any extra memory but it's a much better Operating System. For ultimate game compatibility, you could even get a Kickstart ROM Switcher with both 3.1 and 1.3 (A500 Kickstart with IDE support added), so if you felt like running some floppy games without needing to use a degrader first you can, easily. I have this setup in my A600 and it's the best.
Here's a little video I made showing my A600 with these expansions (IDE-CF and PCMCIA-CF adapters) running Workbench 3.1 -
http://www.youtube.com/watch?v=aTLvrhlNdycHere's a video on installing an IDE-CF adapter in an A1200, which will be the same process in an A600 -
http://www.youtube.com/watch?v=2fWfqRd3E3EHere's a video explaining one way of transferring ADFs to a floppy -
http://www.youtube.com/watch?v=2fWfqRd3E3E (There are a few different utilities that do this)
I'm sure after clicking on a few related videos you'll soon find out there are lots of different things you can use your A600 for, and they're quite easy to upgrade and expand these days! Check out my A600 with 2MB ChipRAM, Network card, USB, numeric keypad and more -
http://www.amiga.org/forums/showthread.php?t=49670 (All these expansions can be bought new).
Make sure you check out
http://www.lemonamiga.com and browse through all the games. There's plenty of information about most Amiga games, as well as ratings and reviews from members of the site.