SSL/TLS protocol

Do I need to buy an SSL certificate to ensure my customers' security when purchasing online? Thank you

While it wouldn't hurt, it is not required unless you are expecting to accept credit card payments though a 3rd party gateway

I sell online using iPayment and authorize.net.

Yes you will need an SSL, which requires a dedicated IP address as well. I'm sure your webhost is willing sell you both. Typically they charge a premium for an SSL but are willing to install it for you at no additional charge.