Step 1. Ask the person you are giving the money too.
I have done several car purchases where the amount was in excess of $10,000. In some cases the car dealer would only take a cashiers check, with a deposit by credit card or personal check. In other cases they were happy with the personal check. It depended on the policy of the dealer.
In the cases of getting a roof put on my house, a heat pump replaced, or remodeling done, the company was flexible: credit card or personal check was fine. These weren't for $30K but they weren't cheap either.
Cash seems to sketchy and dangerous. Getting multiple money orders seems painful. In either case I would be constantly checking the cash/money orders to make sure I didn't drop some.
If they can take a credit card, then they might accept a transaction that large. They might also have a policy regarding the maximum amount they will accept by credit card, or they might charge an extra fee. They also might allow a split transaction: $10K by one method and the rest by another method.
If the amount of the transaction will exceed the credit limit on your credit card, some credit cards will allow a temporary increase for a specific purchase. You will have to talk to a person to get that increase, any function on the website to request an increase probably will not allow you to boost it quick enough, or to the amount you need.
For you the problem with a cashiers check is that you have to be able to get to a branch to get the check. You also have to know the exact amount to the penny, or they have to be willing to accept a cashiers check for the bulk of the transaction, and a personal check for the rest. My credit union doesn't charge me a fee for a cashiers check, so the cost might be zero.
If you do use a personal check, make sure you have the money in the checking account before you write the check. You have no idea if your request to move the money from savings will beat the transaction from the company.
I have never done a bank-to-bank transfer, so I can't comment regarding speed, cost, or ease of process.
In this entire answer I have been assuming that this is a safe transaction, and that the company is legitimate. That allows both sides to trust that the other side will act in a trustworthy manor.