Depending on the dimensions of your business and your industry specifics, which you could decide to use an affiliate network or to run your application in house. Of course, you can also use both solutions. You need an affiliate platform if you propose to require a vast variety of affiliates for you to track their functionality and simply speak with them. For starters, you can cooperate with a couple of publishers at once and optimize your rules, goals, etc. To track traffic, leads and sales, use UTM parameters.
You can assign a dedicated tag to every affiliate and take a look at their performance in Google Analytics. Based on for you to compare effects.