If you are selling something on your web site then you need some way for people who buy it to pay you for it. There are a number of different ways in which this can be handled.
You can set up a merchant account directly with your bank . You can set up an account with a third party credit card service that will collect credit card payments for you and deposit them into the bank of your choice. You can set up with a provider that handles direct transfers between buyer and seller accounts (for example in Australia bPay provides this service online). You can set up with one of the independent payment services (eg. Paypal). You can choose to use more than one of these.
When it comes to which of these you can choose between, one factor that may eliminate a lot of choices is if you are collecting payments for a digital product or online service. For these types of product the buyer will expect instant delivery. This means that you need the payment processor to tell your site when the payment is successful so that you can release the purchased product. Many of the available processors do not allow for this real time reporting and so products are only suitable where you are selling physical goods where a delay between the payment being made and you becoming aware of it so as to ship the goods is not going to be noticed by the buyer.
When it comes to choosing between the options that do support immediate processing, not all of the alternatives are necessarily equal. Some processes only accept credit card while others accept funding via other means such as linking to a bank account. There is also a matter of how well known the processor is and whether the buyer trusts a given third party payment processor. Some independent payment services require the buyer to have an account in order to be able to make any purchases and buyers are not going to create an account with somewhere they have never heard of in order to buy from you.
The way around some of these issues is to offer more than one way for buyers to pay you. For example if you can accept payments through Paypal and also have a separate way to receive credit card payments you are more likely to have people buy than if you only offer Paypal even if you are in a country where Paypal allow the use of credit cards without needing an account - simply because some people don't trust Paypal.
Integrating each payment solution into your site may take a significant amount of time if there is not a pre-built integration solution already built that suits your situation and so you should investigate the various options thoroughly before you choose which ones to spend the time on.