Hm... you might want to hold off for a bit and see what happens with Sega Forever before you make any purchases, but I'll throw in my input from a current perspective.
The Genesis went through two distinct phases: pre-Sonic and post-Sonic. The earlier phase was typically more gritty/realistic as though they were trying to emulate 80's film/broadcast quality, and most of the games were from the arcade or played like they were (Revenge of Shinobi, Streets of Rage, Gain Ground, Golden Axe, ESWAT, Alien Storm, Altered Beast...).
A lot of Sega fans are nostalgic for this era, myself included, and you'll find that this pre-Super Nintendo era is what people generally associate with the Genesis. However, I think that the very best of the console came after Sonic changed its image. Things got a lot more imaginative and off-the-wall, and the programmers' mastery of the hardware brought out some really great ideas and effects.
Looking at the list on Steam, my Top 10 list would go as follows...
Sonic the Hedgehog (main series; original, CD, 2, 3, & Knuckles)
Shinobi III: Return of the Ninja Master
Gunstar Heroes
Ristar
Streets of Rage 2
Phantasy Star IV
Shining Force II
Alien Soldier
Dr. Robotnik's Mean Bean Machine
Ecco: The Tides of Time
The Wonder Boy/Monster World games are also incredible, but Steam doesn't have Monster World IV, which is widely agreed to be the best one, so I'd recommend grabbing it on the "Wonder Boy Vintage Collection" on PSN/XBLA.
Overall, I think that "Sonic's Ultimate Genesis Collection" for PlayStation 3/Xbox 360 is the best place to start outside of a regular PC emulator, and the unfortunately excluded essentials (Gunstar Heroes, Alien Soldier, Monster World IV) can be picked up for a couple of dollars elsewhere.
Now that Sega's bought the Technosoft catalog, be on the look out for Thunder Force IV, too!
Have fun!
P.S. Most people consider Phantasy Star IV the best of the series, and it can easily be played as a standalone game. Some fan service will fly over your head, but it's nothing that'll detract from your ability to play, understand, and enjoy the experience.
