For the DVDs and to convert your videos use handbrake.
www.handbrake.fr
To record videos from your cable box, you will need a firewire cable from your cable box to your Mac.
Register in apple developers website, and download the Firewire SDK.
From the Firewire SDK use an app called VideoCAP and you will be able to record whatever your cablebox output is.
You will have to record ala old school VHS in real time.