Depending on which country you are conducting business in, there may be regulations to adhere to. These usually revolve around confidentiality and security, i.e. card data.
It is far easier to use third party gateways or the APIs provided by banks through their merchant accounts as you transfer the responsibility for that data to them. PayPal is the obvious one - and there are other similar payment mechanisms, but it isn't an ideal solution in every situation.
If transactions need to go straight into a business account, discuss it with your bank. Most banks have their own or a franchised solution.
We build shops with ZenCart and use SagePay as a payment solution, but I doubt it would be available outside of the UK.
Money being money, it makes money every time it is moved and a lot of people want a piece of that. As a result there are a plethora of options to choose from.
If it was a personal / non-business site, I'd use PayPal for ease. What I wouldn't do is try to build my own gateway.
Don't forget, Cake is just PHP and as such is as easy to deal with as any other PHP website. Choose your gateway provider, study its API and everything will become clear.