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EAC is the best CD audio ripper there is, period. Easily configured to use the FLAC encoder as well... and free, of course.
As for burning, any burning software will work. ImgBurn is highly recommended, and free as well. You can use Nero or anything you want to be honest as when you're archiving the FLAC files you're burning them as data files and not audio files (like CD audio).
I've got 86 DVDs (single layer) with all my 2200+ CD collection backed up as FLACs. Makes it easy to transcode 'em to other formats as required.