Since we are just giving good synergy suggestions, I will take a shot at this as well. So Bayleef››Meganium is weak to fire, bug, flying, ice,poison. A handy Pokemon that can take all these Your trusty Raikou. Raikou takes neutral damage from all and is weakly damaged by flying. Meganium is a very good starter to pick, Although it has difficulties against the first to gyms, it does well against Whitney, Chuck to gyms that the other 2 starters can have difficulties with. Raikou is an excellent teammate, although you can't get it till Morty, it will help you take down a lot of Threats that are named Gyarados. It can take out Gyarados with one hit when used probably and has acces to very powerful moved and outclasses Jolteon and Ampharos because of it's well distributed stats and to be precise it's stat distibution is as good as perfect. It can take down Meganium's main rivals, flying types. Not to gorget not many types resist electric types. Since you are playing heartgold you are very lucky to have acces to Arcanine. It has powerful moves and is easy to get in HG. again it covers Meganium's weaknesses. Especially fire atacks because if you are able to get a Flash Fire Growlithe, you can let it switch into any Fire type Pokemon that is threatening Meganium. Not to forget that it scorches bug Pokemon with no mercy. It also has acces to crunch which means that you are save against Elite 4 Will and gym leader Morty. It can scorch Pryce with it's fire type moves and Meganium can take on Piloswine and Dewgong due to it's bulk and acces to powerful grass type moves; Giga Frain, Magical Leaf, Petal Dance,...
Now we have to get rid of the ground (Raikou and Arcanine) and rock (Arcanine)weakness. Well Meeganium is weakly damaged by ground type moves and because of it's bulk, it can easily switch into rock type moves. There aren't many rock types in HG/SS and the main rock types are the geodude evolution line which it can usually take down in one hit due to the 4X weakness to grass. For ground immunity in case Meganium is of low HP to take another ground type move, there are a lot of handy flying types. Crobat is fast and powerful and is weakly affected by poison type moves and can also not be poisoned. This is very good for Elite 4 Koga and team rocket. It has acces to Cross Poison and is a good Fly abuser. It makes catching legendaries easier with mean look and confuse ray is nice for trolling Pokemon. Bite is nice for hitting more ghost and psychic types, just for the extra fun. It also covers Meganium's poison weakness and Arcanine's ground weakness
Now for a great type that can damage a lot of Pokemon and make the life of poison, fighting types miserable, a strong psychic type Pokemon. A immediately think of Alakazam and Espeon. Very similar they have high Speed and Special Attack, though Alakazam exceeds Espeon in those aspects. If you can trade Alakazam is a good option. if not Kadabra is still a very Powerful Pokemon that shouldn't be taken lightly. Espeon is easier obtainable although it can be a pain raising it's happiness. They both cover Crobat's psychic weakness which can usually OHKO it.
The last Pokemon is the dragon killer also known as Mamoswine. It can destroy Lance with just ice shard when holding a muscle band. Mamoswine can also learn surf but this isn't recommended because of it's superior attack stat that you would like to take advantage of.
Now you may ask, but I don't have a surfer. This is indeed true. This team works very well but you need a surfer.
You could always replace Crobat with Togekiss. it can learn psychic, shadow ball and extrasensory which means that Espeon and Kadabra are no longer needed. You now have time to get gyarados on your team though I recommend Kindra over Gyarados since it isn't weak to Electric. Kingdra is not easily obtainable but when you have it, it works vey nice. He can help take down Rock types, ground types , fire types, dragon types, flying types (with Ice Beam) and ice types (with Flash cannon making him a great Powerhouse.
This is my synergy team suggestion. If anything is unclear feel free to leave a comment