Personally, for spoken English, I (native AmE) would simply say "I need to/should/must add some money to my account" (the exact wording depending on the sense I want to convey). Possibly also "put some money in". This assumes that you don't intend to specify the amount or the purpose of the money (I'm assuming that from the way you worded your sentence). "Sufficient for my needs" can be assumed to be understood--why else would you be adding the money?
Most of the other words you listed (replenish, refill, fill up, recharge) carry the sense of returning a thing to a specific (possibly previous) level. "Fill up" a gas tank; "recharge" a battery; "refill" a glass. These could be appropriate if you were replacing funds used off a gift card, but not if you are talking about putting money in, say, a checking account. "Top up" may be an exception; I think it is more British English, although it may be becoming more common, generally. I have always assumed it carried the sense of "refill", but I'm not as familiar with its nuance.
Credit is the correct term for adding a positive amount to an account balance (debit being the opposite), but it's not a term one is likely to use conversationally in that sense (and people tend to be confused about its meaning--blame credit and debit cards). It could be used in a more formal sentence: "Please credit this to my account." However, in this context it carries the sense of how the money is accounted for, so it would be the bank doing the crediting, not you: you give them the money, they credit it to your account.
Edit: from the comments on the question, "deposit" also works well. "I need to deposit some money in my account." This assumes we're actually talking about a deposit account (checking, savings). Technically, you probably shouldn't say that you are "depositing" money to a gift card, but it would be understood.