I'm trying to go into iOS app development. Should I bother with Objective-C or is Swift the new way to go?

Swift, it's easier, visually it looks better and it's the language that Apple will support. Objective-C will not stay longer than 3-4 years.

That said, you will probably need to learn Objective-C at some point if you want to get a real job as an iOS dev.

Thousands of companies have large code bases written in Objective-C, and not many people are rewriting stuff that works for fun. There are also many resources out there that are in Objective-C so it's useful to be able to understand its syntax (tutorials, 3rd party libraries, etc).

I recommend you learn swift, master it, and then learn Objective-C a little bit.

use cordova so that you can have all worlds

Swift.

Objective C is still a thing, but won't be for long. If you're building from the ground-up, Swift is what matters.

If you're walking into an existing codebase at a job, it's probably in Objective C, so at least familiarize yourself with its shitty syntax and frustrating parameters... Then tell your PM it needs to be re-written in Swift.

Both have their applications. Definitely won't hurt you knowing even just the basics of objective-C; that way if you ever landed a job where you needed to do both, you wouldn't be at a complete disadvantage.