Welcome to the forum.
First, you must be sure that your app will provide more functionality than a website. Otherwise it may be rejected from the appstore. And it would not be worth the effort.
-> See appstore guidelines 4.2 Minimum Functionality https://developer.apple.com/app-store/review/guidelines/#design
For the stack, you should probably use Xcode and SwiftUI (you could use UIKit but I understand your app would be well suited for SwiftUI development).
Budgeting: do you intend to develop yourself ? Then budget is mainly your training time to learn to develop.
If you subcontract, the general rules for subcontracting a software development will apply:
- cost will be very variable from one developer to another
- make sure you keep all the rights and submit the app yourself to the appstore, not by the developer
- and gat all source code, documented properly, to be able to continue if you decide to change to a different developer.