Birmingham Airport → New Street Station (Sunday around 18:00) – best direct option?

Hello everyone,

I’ll be arriving at Birmingham Airport on a Sunday around 18:00, and I’m trying to figure out the most direct and hassle‑free way to get to Birmingham New Street. Ideally, I’d like to take something like:

1. A direct train (no changes)
2. Or a direct bus/shuttle if trains are limited

I want to avoid having to switch more than once.

Also:

3. Should I book bus/train tickets in advance?

4. Then onward to Wolverhampton — I see there’s a train roughly every 10 minutes. Is it essential to book that in advance too?

Thanks a lot for any advice ! 😄