There are a number of services that will rip CDs for you. SlimDevices provides such a service, and a quick Google for "CD Ripping Service" will yield a number of additional resources. You'll need to query the companies directly for details on how they perform their ripping, but I'd assume that any that offer lossless formats will do so with some measure of reliability.
If you choose to rip yourself, then EAC is a fine tool and will provide good results. However, the actual performance of the tool is very dependent on the hardware used (e.g. some CD-ROM drives will only rip at 3x using EAC, while others run at 16x and greater) which might be a consideration if you're planning to purchase new hardware for this purpose. Also, each drive has an optimal read offset value that must be computed and configured into EAC for the rips to be completely accurate. AccurateRip can be installed along with EAC and will provide the correct settings automatically for your drive when a key disc is ripped.
If you choose to rip yourself, then EAC is a fine tool and will provide good results. However, the actual performance of the tool is very dependent on the hardware used (e.g. some CD-ROM drives will only rip at 3x using EAC, while others run at 16x and greater) which might be a consideration if you're planning to purchase new hardware for this purpose. Also, each drive has an optimal read offset value that must be computed and configured into EAC for the rips to be completely accurate. AccurateRip can be installed along with EAC and will provide the correct settings automatically for your drive when a key disc is ripped.