All the games listed so far are definitely great starter titles. Drac X and DE2 are the more pricey among these, especially DE2. You can find Drac X for $70-80, and I think that Rising Stuff has a copy in that range right now. As for DE2, it might be good to start off with Dungeon Explorer first since it's much, much cheaper and such an awesome game.
Other games that I'd recommend are:
1. Nexzr/Nexzr Special (Summer Carnival '93): Awesome Naxat shooter. The only difference between Nexzr and Nexzr Special is that the latter has the cut-scenes removed, but added a time/score attack modes. Nexzr Special is also generally cheaper, but you can score deals on Nexzr.
2. New Adventure Island: A terrific rework of Wonderboy.
3. X.E.V.I.O.U.S. - Best game for the Duo....hehe. jk. I love Xevious, but I wouldn't recommend it as a starter game, nor is it the best game for the Duo.
4. Dungeon Explorer
5. Splatterhouse
6. Galaga '88/'90 - An example of a sequel surpassing the original.
7. Salamander
8. Marble Madness - Sadly this was never released. I was just browsing sunteam_paul's site for games and came across Marble Madness. My heart skipped a beat when I saw "Marble Madness" in the "M" section. lol
Well, I would definitely be recommending this game if it had actually been released.
Here's a link from sunteam's site:
http://www.pcengine.co.uk/Images-Artwork/ART-Marble_Madness_Preview.JPG