hi Lima, the easiest (but not the cheapest) way to go is buying some 'Golden Age' (late 50's--early 60's) reissue jazz from some of the mail-order companies. these recordings have typically the best performance and recording quality and most of them are superbly remastered.
i would start with the following 'icon' recordings;
Kind Of Blue, Miles Davis
Time Out, Dave Brubeck
Know What I Mean, Cannonball Adderley
Mingus Ah Um, Charles Mingus
Armstrong/Ellington, Recording Together for the First Time
these are all on Classic Records and you simply can't go wrong with these. if you like these you can then explore other recordings by these artists from this period and in this way expand your horizons one step at a time.
there are other reissue labels that are very consistent with quality recordings such as Analog Productions, 4 Men with Beards, and Alto Analog that you are pretty safe with.
as far as pop/rock music it is really a taste thing but what you are looking for is pop/rock that was originally well recorded......here there are literally millions of fairly good used records to choose from.....i might start with any of the Joni Mitchell, Steely Dan, Eagles, CSN, and Neil Young.....which are all typically fairly well recorded and mastered relative to much other stuff that is out there. of course, Pink Floyd is pretty much a no-brainer if you are a fan. on pop/rock the original recording and mastering is most times the best availible but you need to do a little research to know for sure. you can probably go to a used record store and find 'acceptable' used copies of many of these recordings.
there are some more recent recordings that to me are very good such as;
Famous Blue Raincoat, Jennifer Warnes
Come Away With Me, Norah Jones
Breaking Silence, Janice Ian
these are all personal favorites of mine.
i don't have the knowledge to recommend classical records......but if you want to go down that road a little you can't go wrong with the Classic Records reissues.....maybe buy a few to see what you think. a couple enjoyable no-brainers are;
Sheharazade, Reiner, CSO
Pictures At An Exhibition, Reiner, CSO
this is not mean't to be any comprehensive plan but more a 'get started' plan to get your feet wet. 6 years ago i was exactly where you are with exactly the same questions.....good luck and enjoy the ride.