Question about SATA-oriented DVD drive

Recently, I felt the urge to finally order a DVD drive to fill that empty bay that's been sitting there on my tower. Anyhow, it arrived a few days ago, so I popped open my computer's case and slid the drive in.

My system's board is PATA oriented, and as I attempted to connect one of my unused PATA power connectors to the back of my new DVD drive, I realized that my new DVD drive needed a SATA connector, and my PATA connector wasn't going to work for me.

Here's where my problem comes in. I need a SATA connector, but my CPU is PATA-oriented. I'm considering buying either a SATA host adapter that would attach to one of my open PCI slots and hooking up the DVD drive to that, or buying a 4-pin Molux-to-SATA converter (which would plug into one of my empty PATA power connectors and could then plug into the SATA ports on the back of my DVD drive). I have two questions.

One, should I get that host adapter or the converter? The converter is obviously cheaper at only about five bucks, but I'm not quite sure if it would work.

Two, if I decided to use the host adapter, will I be able to run both PATA and SATA on my motherboard at the same time, and will the DVD drive work if it's hooked up to the host adapter?

Any helpful suggestions are appreciated.