Which is more benefit? promoting affiliate programs from other sites or promoting my own product?
Each has it's own benefits and disadvantages. When you're just starting out then promoting other people's products is the ideal option because it will not require a big budget to do it. Product creation requires a good budget not to mention the promotions as well.
So it depends on the level you're at, are you a beginner or are you already generating cash online? Or do you have enough cash to create your own product?
Creating your product requires a website, hosting, product tools (software), autoresponder, support, design (website, product and affiliate tools), payment processor etc.
Do you have the time, money and resources to do all that?
Should I build a landing page to offer my own products?
Either way you'll need a squeeze page to collect emails. Even if you're promoting other people's products it's a wise move to build an email list so that when you start selling your product you already have people you can sell to.
So start by promoting affiliate products, build a list then create your own product later when you have more experience in internet marketing.