When I started gaming it wasn't on AD&D, it was West End Games Star Wars,
So at least 1987
TSR Star Frontiers, Top Secret, Shadowrun 3rd Edition,
Now we're up to at least 1998 for SR 3E
Werewolf the Apocalypse, Vampire the Masquerade. It wouldn't be until about 4 years into my gaming tenure when my grandmother would purchase the blue and red box of original DnD for me complete with the crayon to mark the dice with.
So now we're at least up to 2001 when your grandmother bought you an 18-year old version of D&D? Was she at a con when she did that?
Your described timeline is kind of a puzzle but alright.
Having begun my RP experience with systems that offered generous character options and variability. I disliked the limitation of AD&D where humans only actual benefit was they could progress through a class for a bit, then could restart progression in another class, and there was no limit to their progression, however, no group I ever played with followed that proscription, and for every 40th level Human 20 rgr/5 fgtr/ 5 rogue/ 5 mage/ 5 cleric there was a 40/40/40 Elven multiclass that shouldn't have ever been allowed.
You were playing AD&D after you received the Basic/Expert D&D sets? Because B/X didn't have
any multiclassing rules.
I didn't get into DnD until 3rd Edition where some of Ed Greenwood's characters in his novels finally made sense statistically. And I adored 3rd edition, it allowed me to create the fantasy character I wanted to play in an easy to delineate manner.
Cool, a lot of us had a ton of fun with 3E. Per-level multiclassing and a unified experience table was a huge innovation at the time. Even if it led to some of the worst breakages later on, it was still a great idea compared to what we had before.
Then came fourth edition which eliminated everything great about 3rd Edition but tried to turn the system into a tabletop World of Warcraft, a system I promptly demonstrated the idiocy of its lack of thought with by building a fey aspected warlock with a cape of the mountebank which let me basically deal damage and teleport, the damage and teleport, and when the GM tried to be clever and isolate me then I used the cape to teleport me back behind the line the party had formed, the whole system was stupid, not to mention the abject horror they turned the Forgotten Realms into.
You're a few years late for the Edition Wars. Many here remember them but few wish to reignite them.
Then I bought the 5th Edition players handbook, It seemed to actually streamline the 4th Edition and make it less a tabletop MMO while bringing back the simplicity of the old school blue and red boxes. However what drove me to ignore the rule set was that fundamental lack of variability that 3rd Edition actually offered. It seems like I'm pretty much stuck in the class I began the game in and I can either choose a mediocre stat bonus where I used to be able to alter the standard progression path by taking a feat, and the stat bonus would come later which demonstrated a focus in a differing area of my character's priority.
You can still multiclass in 5th just like you did in 3rd. There are still feats. There are now backgrounds. There are not as many options overall as in 3.5 for two reasons: 1) it hasn't been out for anywhere near as long as 3.5 and 2) There's a deliberate design choice here not to flood the market with rules expansions as they did with 3E and 4E.
So, why should I play 5th Edition? It eliminated the wonderful options a player could take his character and even it's weak multiclassing can't portray the most famous characters of our favorite DnD novel characters. I mean, stat out Elminster the way he should be in 5th Ed, or even Mirt the Merciless.
One, if you have a group of players who like 3rd edition D&D why would you ask strangers on the internet to convince you to change to a new edition? If you don't have that group anymore but have found a new one that's playing 5th, well, is a game in a new system you're not sure about better than no game at all? The best way to learn about a new system is to play it.
Two, if your measuring stick is how well it reproduces characters from D&D novels it really depends on what you want them to be and I don't know that any version of D&D is going to make you happy. Heck, I'd say Hero system might be your best option for that!
Three, this edition has been out for 3 years now. There is a load of reviews, recaps, podcasts, and actual plays out there. If you still aren't sure about it, see if there's an AL group near you and go watch or play a game there.
Bonus: If you're that serious a 3E fan and like the options and detailed support it had I would think you would be looking more at Pathfinder. Seriously, it sounds a lot more like what you're looking for. It looks like you're in Aggieland so I am sure there are some PF groups there too, mixed in with the 5E crowd.
Regardless, good luck, and in my experience the group often matters far more than the rules set they're playing right now. Hopefully you can find one and have some fun.