This has nothing to do with Hi End or not Hi End. Even "newer" vs. "older" or "cheap" vs. "expensive" does not matter.
From my own experience, I blame Liteon to neglect CD burning capabilities.
I do own a JVC UX-T1 which was not designed to handle CD-R media. If I burn an audio CD with my Liteon (Sony DW-G120A @ Liteon SHW-165P6S), this disc is unreadable by this unit. Burning the same media at the same speed selected with my Pioneer DVR-112, the UX-T1 can play that disc.
Admitted, this is an extreme example for real world testing.
If I'd test these discs, then I can see significant differences for C1 errors and jitter (Liteon jitter is much higher).
http://club.cdfreaks.com/f77/cmc-75424/index4.html#post2143613 (does not play - and the CD-R capabilities of that Samsung is much better than those of a Liteon)
http://club.cdfreaks.com/f77/cmc-75424/index4.html#post2143620 (does play)
Or look at this (Liteon vs. Pioneer):
Since you indend to buy a new, modern head unit, you might not run into that issue. Playback of CD-R should be much better nowadays.
Will I need to invest in a better drive to get the perfect copies I'm looking for?
At first, use what you have. In case, your discs are unreadable or playback skips, then consider another drive for burning.
Also, will using this drive for my ripping cause any issues with audio quality, or would it be the same as any other drive?
These drives are rather good readers, so there is no need to use another drive.