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Best to talk with your Tax Preparer about this. I suggest H&R Block Executive Tax Services. They're highly competent. If you're a US Citizen you're taxed on 100% of your global income anyway. If you haven't been paying tax on 100% of your income, your best action is to immediately work with your Tax Preparer + file tax amendments for last three years, declaring your income + paying back taxes + penalties incurred. If more than three years apply, then ask your Tax Preparer how to handle this. Rule of thumb: Trying to evade taxes is a serious matter these days. If amounts are large enough, you can fall under RICO (money laundering laws). You don't want this. Start as a Sole Proprietorship + talk with your Tax Preparer about your specific situation to determine if another entity might be useful (Corporation). If you're making a truck load of cash, read up on Transfer Pricing + consider having your income for this enterprise flow into an IDC in a non-US jurisdiction.

When you open a bank account for your corporation, you'll need to make an initial deposit with your personal funds. A shareholder's initial contribution can be recorded as either debt or equity. If you want to record the initial contribution as equity, you would debit cash for the amount deposited into the bank account, and credit an equity account, such as “shareholder’s equity” or “capital stock”. Alternatively, you can record the deposit as a shareholder loan. Debit cash for the amount deposited, and credit a liability account, such as “Loans from Shareholder”. There are also methods to bifurcate the contribution by recording a contribution as a combination of debt or equity.

If you're not an American or Canadian citizen + you have no physical location, you only pay your Estonian taxes.

I did not actually have too much experience with bookkeeping platforms before. But we stick with Xero and there is no reason why I should look for another option.

You can fund your new Corporation bank account by depositing personal funds into that Corporation account for initial capital for the business. That investment can be classified as a loan to the Corporation or may be for issued stock shares of the Corporation (a needed conversation). I can help you set up ta chart of accounts, based on your specific business, which can be used by any accounting system but I mostly work with QuickBooks Online. (Message me for a referral to a Xero bookkeeper if Xero is imperative.) Best wishes!