VISA credit cards are your best bet because all online casinos that I know of accept VISA deposits and process the money to your player account instantly. It's also the convenient way to deposit money to an online casino since adding your credit card's details is all you need to do. (After making your first deposit, you'll be able to make a credit card online casino deposit with just a few clicks.)
Mastercard and American Express credit cards are often accepted but certainly not as often as VISA cards. Furthermore - epecially in the US - VISA-branded credit cards have had the highest success rate at online casinos that accept other credit card brands as well. In short: it pays off to have a VISA credit card because it's the most widely accepted and has the highest success rate.
Credit Card Deposits Are Fast and (Often) Free
Making credit card deposits to online casinos that accept credit cards is often free - meaning that the online casino in question charges no processing fees for taking your deposit. I have no idea if the credit card company charges you for the transaction - that depends on the terms of your contract. So not only are credit card online casino deposits instant and convenient - they're often free as well.
Here's a little-known fact: debit and gift cards usually work just as well as credit cards (of course a gift card requires more work since you have to buy one each time you want to deposit money to an online casino). But it has to be the right kind of a debit or a gift card - for example, gift cards must be eligible for international and online purchases, and the problem is that not all of the debit and gift card types work. As an example, Vanilla VISA debit cards fail to work now even though they worked before but Netspend debit cards still work.
Remember to Consider Cashout Times
But the fact that depositing to credit card online casinos is all those things means little if getting money out of the casino is difficult or takes a lot of time.
The intention of playing with real money is obviously winning money and making profit, and in case we do, it sure is nice to get the money out of the casino as fast and conveniently as possible. Paying attention to withdrawal methods, times and fees is therefore important. Especially for US customers, since some online gambling sites have taken several weeks if not months to process a cashout - those are the online credit card casinos that we should stay away from at all costs.
In the US, the most common withdrawal method (and usually the only possible method if you've deposited with a credit card) is a check and those always take some days to process. An acceptable check withdrawal time is a few weeks but casinos like Bovada deliver check payouts in 7 days right now - which is a tremendous achievement since they're a popular online casino and have loads of checks to process - for US players, this is obviously an important consideration. (I recommend Bovada.lv anyway since they have 15+ years of experience and a strong track record throughout that time, plus fair games, of course.)
Outside of the US, there's less need for payout considerations since you have more withdrawal methods that can be processed faster. You may even be able to withdraw the money back to your VISA account, which is as convenient as depositing money to and withdrawing money from an online casino gets right now.