HeartGold is the remake of Gold, from the Gold/Silver generation. It’s actually quite a fun re-imagining of it, with the modern-day Pokemon technology added in (touch-screen control, a new sudoku-like minigame, wifi trades!).
As for your question @Vincent_Lloyd, I consult Marriland’s online pokedex entries for Jolteon and Eevee. Since your goal is to learn Charge Beam, the pokedex says that Jolteon learns it via TM57 whereas Eevee can never learn it, so there is no difference in terms of how fast it would naturally learn it (in previous games, less-evolved pokemon often learn moves at faster levels than evolved ones, but I’m not sure if this is right for this generation of game).
So the differentiator becomes, as @Mariah says, what other attacks you want your Jolteon to have, and whether you need to leave it as an Eevee until it acquires them or whether you need to evolve it faster in order to not miss the chance to learn the move. One important thing I’m thinking here is Baton Pass, which Eevee learns at 36. Since Jolteon is very very fast, you will likely be the first to attack each turn. Since Charge Beam raises one’s special attribute by a level, Baton Pass can allow the Jolteon to swap out with a different Pokemon but to keep that new pokemon’s Special attribute boosted, which can be a really really awesome and match-changing moveset, especially if your Jolteon is now up against a rock-type Pokemon and you have a water-type Pokemon in reserve.
Another factor to consider is whether you will use your Eevee/Jolteon in battles before it is ready or if you will wait and train it passively via the Pokewalker or Exp share. Jolteon’s stats are way better than Eevee’s, so evolving to Jolteon may be a proper decision to make if you intend to not go the Baton Pass route and instead go for a super duper electric fryer Jolteon. That way you will gain his electric movesets at appropriate times and be able to use him as a part of your Pokemon journey, and he/she will kick ass.
If I were in your shoes, and I have been as I totally made an Eevee army once, I would decide if I needed Baton Pass or not. Eevee doesn’t really have access to any other moves that would make a stronger Jolteon, so if I did not need Baton Pass I would evolve Eevee at Level 1 but I would probably put some strong electric-move TM on it at Level 1 since Jolteon learns Thundershock at 15, Thunder Fang at 43, the non-offensive Thunder Wave at 57 and finally Thunder at 71. In fact I would put TM24 (thunderbolt) or 25 (thunder) at Level 1, so that it can kick some serious ass and get up to the level 20s faster.