You have two basic choices, either a stand alone CD-R or a computer based recording/editing software with an integrated CD burner. Each method has its benefits and either method can produce quality results, however, the computer based method offers greater user control and when optimally setup, will outperform a stand alone CD-R.
There have been several threads on CD-R units. People seem to like the HHB, but Sony and Yamaha also make high quality units.
I am currently transferring part of my vinyl collection to digital and I am using the following setup. An Apogee A/D converter into an Apple G4 via an RME soundcard. The recording software is t.c. works Spark XL. On occassion I will apply "corrective" EQ to what I consider a poor recording, but more often I use a declick algorithm to clean up the surface noise on older records. It won't make a badly scratched record sound like pristine vinyl, but it will remove most of the crispy/crackle artifacts.
The key to the transfer process is setting the correct signal level into the A/D converter. Set it too high and there's a nasty type of distortion. Set it too low and you loose bit resolution. It's my experience that I can produce digital copies that are sonically better than many commericial remasterings. (This was not the case when I used a Yamaha CDR1000.) The transfers are not indistinguishible from the originals, they are inferior, but not dramatically so. The loss in quality is apparent in a direct A/B comparison, but not otherwise.
Regarding HDCD, I know of no consumer oriented product that performs the encoding. You might be able to find a used converter in the $10k range. As such it's not a good value when compared to the Apogee UV process or any of the software dithering solutions.