Bitrefill works with all wallets. We don't endorse any specific wallets, but here is a great resource on how to choose a great bitcoin wallet and here’s an article on how to choose a great multicoin wallet. There are also wallets listed here at Bitcoin.org
Also, to avoid transaction fees, you can deposit bitcoin into your Bitrefill account for instant, no fee transactions. Your Bitrefill account is not a wallet but this is a great option for recurring customers that want to save on fees and their waiting time when making frequent purchases.