If you'd like to disable Photo Stream on your iOS device, go to Settings > iCloud > Photos and switch off "My Photo Stream".
As for the personal stream with photos being uploaded manually, you can, in fact achieve this.
I find that the easiest way to do this is to first go into your Photo library and select the photos that you want to upload.
After that, select the "Share" button (the one on the bottom left corner of the screen) and select "iCloud".
You'll be greeted with the screenshot below. Select the button that says "Stream", then "New Photo Stream".
Type out the name that you want to call your Photo Stream.
You'll now be greeted with the screen where you type in who you would like to share this Photo Stream to. Leave this blank. Click "Next".
After that, you're done. I'll let you know that you can also add videos to photo streams as well. To add, remove, or modify photos and videos, go to Photo Stream and select the Photos Stream that you created. Everything should be self-explanatory after that.