I used to use a program called "Relockick" which loaded in a KS1.3 ROM and also "Degrader" is another option. Be aware that these programs do not work 100% and take up memory which can cause other issues.
If you have extra memory in your A600/A1200 then look at WHDLoad which works very well. A 3GB Hard Drive will have more than enough room to store all of your favourite games and the replacement Kickstart ROM files.
I use WHDLoad on my A4000, Minimig, Chameleon64 and FPGA Arcade.
Assuming you have extra RAM, the easiest way to go about using it is to download one of Bloodwych's ClassicWB packs (the "Lite" one should do OK for your A600 or the FULL or OS3.x version for your A1200. Create your working hard drive, track down and install teh kickstart ROMs into your DEVS/KICKSTARTS draw, download KillaGorilla's pre-packaged game packs and extract them into the GAMES draws... and be prepared for some sleepless nights and overworked wrists.