I always try to obtain inspiration from other games, specially the professional ones. I gonna analyze some monster breed games (and Beyblade)
- Pokémon Mystery Dungeon: You have a big quiz to determine what is your starter (from 18 or 22 in the sequel). After, you can select a partner (between 10 or 13 in the sequel. It must be from a different type than starter). I didn't like this one, because a lot of players will reset to get specific pokémon. You are a human transformed into a pokémon.
- Digimon World 1: At start, you are asked if is day or night. If you answer day, your starter is Agumon, else your starter is Gabumon. After, when you Digimon dies, you need to select between 4 eggs that always have the same Digimon. Makes sense receiving one, since the game works like you are the "chosen one".
- Digimon World 2: You will choose one guild/clan to take part. Each one was a different starter. There is a type triangle Vaccine>Virus>Data that is basically like Hero>Evil>Common.
- Digimon World 3: You can select a team with 3 starter digimon, between 3 teams. They are based in balance, powerful (offensive) and maniac (hard to raise). The game is a game inside game, so a starter makes sense
- Digimon World DS/Story: Similar to Digimon World 3.
- Dragon Warrior/Quest Monsters: You start with Slime, the weakest monster. I like this one, because this encourage the player to seek better monsters. You receive a starter to do a favor for someone
- Dragon Quest Monsters Joker 1: You can select between Dracky, Mischievous Mole and Platypunk.
- Dragon Quest Monsters Joker 2: A random between 6. You find it stored.
- Monster Rancher: The series have a interesting concept: You can generate monsters (from hundreds) in a shrine putting a real-life CD (games, musics, any CD) and reading. Some specific CDs have rare monsters. In some games, there is also some options in the market. Since you are a professional tamer that even have an assistent, makes sense having these things. Barring fusions and special cases, all monsters are obtained this way.
- Monster Rancher Advance: Like the main series, but instead of a CD, you can put a word. When you progress in the game, more character are allowed.
- Monster Rancher DS: Like the main series, but instead of a CD, you can draw in touch screen.
- Metabots/Medarot: There is a Kabuto version (Metabee outside Japan) and Kuwagata version (Rokusho outside Japan). Your starter depends the one that you are playing (like Let's Go, but 20 years before).
- Yu-Gi-Oh! Monster Capsule Breed and Battle: Besides exceptions, the only way to obtain monster for this game is selecting between 6 eggs that produces the same monsters.
- Azure Dreams: You always start with Kewne. A good starter. You find it in the way (makes sense in late game).
- Beyblade: You can select between 2.
For
fangames. Notable mentions:
- Survival Island: You can type a pokémon name and get it first forms. Legendaries are forbidden
- Splice: You can get Arenay, that can change form like Silvally, but with more different sprites.
- Uranium: You have to choose between 3 starters like a standard game, but you take a quiz before that points the one who better fit for you.
- Red's Journey West: You start with Shuckle. You receive one in Cianwood, like in GSC.
For me, while I like the Dragon Quest Monsters approach of a weak starter, it isn't popular. I like the pokémon with branch evos as starters, but almost all existing ones aren't good in my view. Eevee is a good one, but is a 2-stage pokémon and for 3 just change the item that you buy. Maybe if you put the items in different points in the game, the player can wait or use the one that he found first, so, for example, you can put like a Fire Stone first, since Flareon is the less popular.
Maybe I make a Tyrogue-like fakemon with 3 stages and better conditions between evolutions, like never fainting for one, fainting more than 10 times for other and a between.
For the lore, you can give it like professors do, make character receive money to buy it or even receive as parent gift.