When you buy on gun broker, it is up to the seller how they will accept payment. Some will take credit cards, some only checks. Most will list in the sale what method of payments they accept. If they do not take credit cards, the safest alternative is a post office money order. I think you need to pay for those in cash at the post office, but it's much better than a personal check, and you shouldn't have to wait for it to clear.
https://www.usps.com/shop/money-orders.htm
The seller should give you the receipt. Your FFL is only concerned with the transfer. You will have already paid for the gun by the time the FFL receives it, it will already be your property. The FFL's role is to just transfer legal possession of it to you. Most of the time the FFL will have no idea what you paid for it. If the FFL charges sales tax, it should only be sales tax on his transfer fee.
Normally this is what I do. I call, or stop by, or sometimes email an FFL. I will tell them I am interested in buying something online and I ask if they do transfers, and how much, and if there are any additional fees they charge. I also ask about their policy of accepting shipments from non-FFLs. If they are cooperative, and if their priceis fair, I will buy the item online. If its an auction, like gunbroker, once I 'win' the auction, the seller usually sends an email with instructions. If I don't see an email in an hour or so (given normal business hours), I will call. I will then CALL the FFL to tell them I have purchased something online, I plan to use them to do the transfer. I communicate to them the instructions that the seller has given me. If I have an email of the instructions from the seller I will offer to forward it to them.