Mom has a DVD/VCR player, what should I do?

We're planning to get a new 42 inch plasma HDTV, and I have an updated PS3 already to use for playing blu-ray and ofc gaming. My mom still has an old VCR/DVD combo player, and a small collection of VHS. What I want to know, is a. Is there a cheap, easy way to convert my moms VHS movies to DVD/BD? or b. where can i find an affordable, good quality component cable to hook up this piece of junk to our new tv?