I love the Bombcast but I was disappointed with the crew's answer to Nathan's question about The Legend of Zelda and Final Fantasy. I believe that one of the worst things about video game culture is the obsession of what's new. Everybody should play old games. If you don't know why, I can answer that another time. Anyway here was an exciting opportunity for some industry vets to turn a gamer on to some old classics, and I feel they dropped the ball a little. It wasn't a bad answer so much as not an answer. LoZ was treated better than FF at least.
Nathan, if you're reading, I tried to give as much information as somebody interested in these games would care to read. Hopefully this inspires you to go learn more about these games and hopefully play a bunch too.
If you want to play Legend of Zelda and you never have before:
There are some options. It depends on what consoles you have available to you, whether you have a PC, and how good you are with emulators, etc. I'm skewing this to what I think is the most viable. I don't have much different to say than the Bombcast as far as this series goes.
Ocarina of Time was at one point the highest praised game I could think of. Not sure if that reputation is still around, but this is a golden oldie for sure. The version available on GameCube holds up best if fuzzy graphics bother you. You get it packed in with Wind Waker, which is an amazing 2 for 1 deal. As they mentioned on the podcast these two games are quite similar, so I wouldn't play them back to back. To be fair, Link to the Past is also very similar (and by very I mean extremely) similar to OoT. But the perspective shift is enough to make the experiences unique. Majora's Mask is probably the most unique LoZ game, but it's hard to gauge how much that would matter to someone in your situation. Worth playing for sure, but you'll need an N64. You'll need an SNES or GBA. I'll wrap this up by saying that you could do worse then pick up a GameCube and SNES to play these games. The former is an underrated console with some real gems, and the latter, well -- do I need to justify the Super?
If you want to play Final Fantasy and you never have before:
Too many versions/editions/releases of all these games to list here, so you'll have to Wiki that.
I, II and III are very simple games and probably won't hold your attention unless you love FF or old JRPGs. Check them out later.
IV and VI tend to get the most praise from hardcore fans and those who never liked the series after the 3D jump. Both these games are really awesome despite their crotchety fan-base. The graphics are simple but have tons of character, great art and fantastic enemy design. Sound and music is great (as it is throughout the series). VI is known for being especially dark. I don't want to spoil anything for you, so I'll just the villains in this world walk the talk.
V has a robust job system, but this might be my least favorite of all. Something about the world and story just never clicked with me. Can't visualize the ending, so it's totally possible I never got there. These older games move slow, but it's worth noting this for all FFs: they basically take 5 hours to get rolling, 15 to get moving. Roughly.
VII is a fine game. It's hard to look at any of those 90s mega-hits-that-changed-games (MGS, Half-Life, Diablo II, StarCraft, GoldenEye, Super Mario 64, on and on) objectively. But there's this weird, weird attitude I run into now where people degrade these games as just "products of their time," "innovative because of their time". Of course that's true but it doesn't need to be a pejorative. VII holds up very well actually. Even graphically: though the polygonal sprites you run around the world with are exceedingly simple, they're clean and well animated, and the pre-rendered backgrounds look great. They pump tons of polygons into the sprites once you're in battle (where you spend a lots of your time, obviously) and they look great, better than VIII and IX I think. Cartoony, but that gives them a sharpness the later sprites don't have. VII also rewards exploration with major plot lines and characters, and that doesn't happen again in the series as far as I remember. The game's plot, which centers on the environment, seems more relevant and grown-up every year.
VIII, which was derided by many as being inferior to VII upon release, is a really good choice too. There's a real scope to the story and the sci-fi world is very well realized. A mopey protagonist (who you'll like more or less depending on your own mopiness level) but great characters all around in this game. Tons of little stories packed away and hidden too -- some great reasons to explore and return to locations, though rarely anything as major as what you find in VII. VIII's characters also have lots and lots and lots to say. More writing in this game than maybe any of the other text-based FFs. This gives you some reason to replay the game itself. Flying around the world map is also great in this game because your sprite is so small and the map so big. Also: time-travelling memories!
IX is a super charming and very interesting game. The last "traditional fantasy" game in this series. Harder than VII or VIII as I remember. At first it doesn't seem as mature as VII or VIII but don't be fooled. This was the last Playstation era FF, and it shows. The level of polish and the amount of content here is impressive to this day.
X is o-kay. Some really, really strong combat mechanics, but a meandering and sometimes boring storyline conflicts with your enjoyment of the game. The introduction of voice-over to the series may be to blame, but this game has a relatively weak cast outside of three of four characters. This a hard one to recommend, though I play it myself now and again.
XII breaks from the mould established by previous games in some big ways, and many gave it a hard time for that. I really enjoyed the combat system, in fact it may be the best. Very interesting sci-fi meets fantasy world, nice feel to the cultures. Unlike many FFs all the disparate parts of this world do seem connected. Unfortunately the principal character is the least interesting. Add to that the game seems to suddenly end, and... you know, complex feelings about this one.
I couldn't play more than a few hours of XIII, so I really have nothing positive to say about it. I haven't played XI or XIV either (they are both MMOs).
I really hope you dive into this series. You'll enjoy it, I'm sure. For my money, start with VII. It's a got a really, really strong, fast start for a JRPG. It just thrusts you into the story and gameplay, which I think is the most important thing for anybody approaching this series for the first time. I'm sorry if this post read a little disjointed, I had to copy/paste a lot as my internet's highly shifty. If you think you can't get past old 3D, go for VI. If you can't do old 3D or 2D, go for XII.
Best of luck!