The thing you have to think about when using the Heroes III Services collectively is whether or not it is worth it in a financial sense. To use the Heroes III Vault you have to both pay the Vault cost and the Deposit fee of the Heroes III Bank. Both of these need to be saved for emergencies and it is never advisable to simply store all of your money in the Heroes III Vault.
Most of the time you should avoid the Heroes III Hospital and allow your account to heal naturally. Though you want to save your Heroes III PlayMesh Points for more important things, you should note that you also have the option of spending Heroes III PlayMesh Points to heal yourself. It is best to use Heroes III PlayMesh Points for Alliance Members, but healing yourself is the cheapest option for using Heroes III PlayMesh Points and may be worth it if the financial cost is unreasonable and you have to bring up your health.