You can actually do both, as affiliate marketing is way different from having your own store and selling through drop shipping.
Amazon Associates earn by referring buyers to Amazon listing/products and they get paid a commission if the customer makes a purchase. In effect, they do not actually sell any product, nor collect any payment from buyers. Their websites will act as a referral engine/marketing. Similar to other affiliate programs, once a sale has been made, Amazon pays the affiliates/associates commission, usually on a monthly basis. The percentage for commission varies per product (I think at max 15%).
An obvious advantage with affiliate marketing is that it is relatively stress free :) You do not need to attend to customer for support, no need to worry about product fulfillment, because once you have referred a customer you just get paid with a commission. :)
Dropshipping products from your own online store entails a lot of work. Even though you are not the one sending or fulfilling the product, since the customers bought from "your store", you need to deal with customer issues - delivery, product quality, returns, etc. That is why choosing a reliable drop ship supplier is crucial. :)
The main point though is that selling through your own online store will help you make more money than if you sell as an affiliate, because with your own store you can set your own profit margin/pricing (as much as 50 to 75%?) as compared with the limited rate to earn from affiliate sales. :)
I'm looking forward to see the home of something quite cool. :)
Best of luck to your endeavor! :)