It's difficult to know these things in advance, of course, so even with the best planning you may need to make adjustments later. However, I'd recommend the following:
You won't likely need a swap partition larger than 8 GB. You have room for it and it won't hurt, but it doesn't make much sense, either, so if I were you I'd keep /swap at 8 GB.
I've had my root partition at 30 GB for about a year, and I'm still using less than 10 GB of it. You might install larger programs than I do, so give yourself a buffer: I'd recommend 20 - 30 GB.
As for the /home partition, that's where you'll store your data and files, including pictures, videos, projects, etc., whatever sorts of things you store and keep. I don't what sorts of things you keep, but in my case my pictures take up perhaps the largest share. Even so, having given myself lots of room (about 300 GB for /home), I have used only about 50 GB. You'll have to decide for yourself, but since you'll use a large NTFS partition to share data with Windows, you can probably get away with 30 - 60 GB for /home, with the knowledge that you might make adjustments later.
As far as space for Windows and its apps, etc., if you think you need 150 GB then that sounds fine. And the rest NTFS to share? That's fine, too. (Eventually you might want to revise that, but it's certainly fine at the beginning.)
You didn't say whether or not you already have Windows installed on the drive, but I assume you do. Windows can sometimes get finicky when being resized. I would recommend resizing your Windows partition first from within Windows itself using the Windows administrative tools, and then you can create the Ubuntu partitions as you install it.