I have already made a native iOS app and I was wondering if the consumers could just download the app onto their phone without jailbreaking or installing anything. I could maybe use a third party app store, but I can't have them download the store app and I need it to use my native app, not a web app. Is this even possible? My alternative is to make the app a web app and put it on a 3rd party web app store.
You can do this, and it's called Ad-Hoc development. It allows you to install on up to 100 devices, from the internet, but there's a catch. You have to get the UDID of every device that you want the app to install on and add it to your ad-hoc provisioning profile before the device will install the app. So, possible, but limited.
Short answer: You can't.
You can't install native apps without Apple's App Store or a developer account's limited ability to distribute test software or an enterprise account's ability to distribute to it's registered devices.
Web apps are completely unrestricted, but have no means to "install". You have to instruct users to save the bookmark on their home screen.
All iOS devices have built-in strong security mechanisms that will prevent any native app from being installed or run unless it is signed by Apple or by a developer certificate. Developer signed apps check with Apple's servers and are limited to 100 devices max per developer account.
So the only way to distribute a native iOS app to over 100 consumers stock OS devices requires your app consumers to buy developer enrollments themselves, at $99/annum, which will make your app very expensive. Or just submit it to Apple and see if they approve it for their store.
Web apps can be installed from any web site, with a custom icon even, and can be run offline, but are limited in performance and functionality.