Any interesting tidbits to really get people wanting to play any of these games, reasons why you are suggesting them?
I'm at work, so I'll pause in between bits and edit this post throughout the day. It will be a fairly large post and slightly comprehensive.
Monster Rancher 1 & 2: The absolute best in the monster breeding/training games. In my humble opinion, at least. There is a small tidbit of a story in these. Mostly so far as you are a Rancher and you are out to raise the very best monsters and become the best Breeder. You acquire monsters in a number of ways. In both titles you can goto the market and select seasonal monsters. Also featured in both, and the primary method, is putting in discs into your PlayStation. The game and console read the disc's data and generates a unique monster for you. In the second game, you can generate monsters from the first game via your memory card saves. Or in today's world, your virtual memory card. The entire series also features monster breeding. Basically you freeze two monsters after having trained them as high as you can get and as old as they can become. Then, you go and combine them. The result is a monster that shares the statistical, physical, and mental traits of both parents. Moves, and the starting amount of them, also translate over into the offspring. Monsters do die in this game so you have to be sure and save when you think they are about to die. You enter these monsters into unofficial and official battles. This is how you obtain gold, rare items, and increase your breeder rank. There is also an adventure type mode in each game that provides the means of not only increasing particular stats, but acquiring new battle techniques to use in the tourneys. There are tons of monsters and even more combinations of those. If you choose to play but one, choose to play 2. It is universally accepted as the very best in the franchise.
Digimon World 1-3: If you aren't a Digifan, you may not like these games. That said, I think they are phenomenal. All three of these have a solid story to them that I have repeatedly enjoyed. The first and third titles have similar gameplay. You are a boy put into the digital world and have to set out and save it from an evil entity or cataclysm. In the first, you acquire a starter based on a few questions once you boot it up. You then traverse File Island and build up the now destroyed town in the center of it. You do this by defeating them in the wild and knocking the sense back into them. Your Digimon grow stronger through training at various facilities throughout File Island and also in battle. The way you train your Digimon is integral to how it evolves throughout its life. If you Digimon does die, you can use its life essence to bolster the life of your next partner, making it even stronger than it would have been. Each rookie stage Digimon has various paths it can digivolve down. Battles are ATB based and in a small, free roam arena. Multiplayer is focused strictly around such battles. Pitting your best Digimon against your friends' best.
In the third title you are a boy set into an actuall Digimon MMO. You and everyone else logged in get stuck into it and cannot return to the real world. You set out with your three starter Digimon to solve this problem and save everyone in the game. Battles here are turn based like a traditional RPG. You can have one Digimon out at a time. However, they can DNA digivolve, or join together, to digivolve into an even more powerful Digimon. You explore the vast world battling as such and engaging other Digimon as you set out to on your adventure. There is also a very nice trading card game that takes place within the MMO. I'd say it even rivals those of Final Fantasy VIII & IX.
The second game features the most indepth story. While the other two are preferred by me for their gameplay, this one easily has the best story to it. Humans and Digimon live in the same world in this title. And you feature an upstart Tamer coming into his own. After the initial rookie test (read tutorial) you go on to learn about and select a faction to join. Blue Falcons, Black Swords, and Golden Hawks. These represent the three main types of Digimon. Data, Virus, and Vaccine respectively. The gameplay here consists of the player running around city or safe areas and interacting with various characters and Digimon. The main gameplay of Digimon World 2 is featured in more of a dungeon crawler style. You get into your vehicle, called a Digi-Beetle (a tank of sorts), and traverse maze-like dungeons. Enemies are onscreen and can be dodged, if you are able to. The battles are turn based and turns are highly reliant on the Digimon's speed. You can have three Digimon in an active party battle. As you upgrade your Digi-Beetle, you can carry even more along with you on the adventure. You Digimon earn experience and level up. This is how they learn techniques and digivolve. However, they hit level caps. To make them stronger and increase their level caps, you have to DNA digivolve them. Basically train two Digimon to their respective caps and combine them. This produces a Digimon of varying type and species based on the two parents. The player selects any and all moves they wish to transfer over or discard. Based on what levels the caps are, the new Digimon's cap is increased. This allows for the player advance them enough to digivolve them to their next, and stronger, forms. Digivolution is permanent until DNA digivolved. Extremely well put together game that I recommend not only for Digifans, but anyone who likes a traditional RPG.
Monster Seed: In Monster Seed you play a Ruler. A person who can control and command monsters. This game has a cohesive story to it. You may or may not find it basic. The way they speak is a little odd at times, but nothing overly hard to understand. As Master Daniel you work to get coin and eventually to discover and defeat the ill events and groups in the territory you've arrived in. You walk around safe areas and dungeons alike in 3D movement. However, the overworld is simply a locale selection tool. You obtain monster seeds throughout your travels and battles. You use these in tandem with temperature settings and hatching materials to produce a wide array of varying monsters. Battles are turn based strategy much like FF Tactics, but with a sort of 2.5D view. That is pretty much the gist of the game without ruining any aspects of it. A classic I revisit.
Final Fantasy Origins, Chronicles, Anthology, VII-IX, Tactics
Chrono Cross
Soul Blade
Battle Arena Toshinden series
Twisted Metal 1 & 2
Vagrant Story
Threads of Fate
Legend of Mana
Metal Gear Solid
Brigandine: The Legend of Forsena
Brave Fencer Musashi
Tomba 1 & 2
Tales of Destiny
Alundra
Shadow Madness
Tobal No. 1
Bushido Blade 1 & 2
Parasite Eve 1 & 2
Ehrgeiz: God Bless the Ring
Saga Frontier 1 & 2
Dungeons & Dragons: Iron and Blood
Thousand Arms
Wild Arms 1 & 2
Megaman Legends 1 & 2
Misadventures of Tron Bonne (Good luck)
