The only experience I have with Orca is on Ubuntu 12.04, so I hope it has not changed much from earlier versions. " it just screams random things at me when opening windows.." agreed with my first experience of the program, but eventually I realized that it really is helpful.
It is intended primarily for folk with less than perfect vision. So it will very cleverly tell the user when the cursor is traversing a button, a link and so on, as well as read textual material -this is the origin of the words you hear which are NOT printed on the page. This serves to help orientate the user 'on the page', so they get some help navigating.
The voice is a huge turn off but you can improve it by selecting better settings in the preferences. When you run Orca from the menu, a small popup window appears on the screen. The left-most tab is Preferences, so click on that. Then a larger popup appears and you should select the Voice tab. About half way down the page are two sliders.
One is labelled 'Rate'. Slide that left so that the value changes to 30. That slows down the speed of the speech. Below that slider is another one labelled 'Pitch'. Slide that left until the value is around 4.0. That lowers the pitch of the voice so that it does not grate on the ears quite so much. We're all different so it really is up to the user to find the settings which suits the ear best, volume included.
I do not doubt that with experience of the voice, the user will eventually want to speed up the voice to faster reading speeds but initially, understandability has to be the prime consideration.
I copied some text into a text editor. The reader announces the name of the document. I determined that the reader will read chunks of text highlighted by use of the mouse: the only thing to watch out for is that the reader says 'selected' after the end of of the selected text is reached. This would be of use to someone who can not see what is happening on screen, as is the title announcement.
This is a good piece of software, tailored to those with a specific need but I see no reason why it could not be used in the manner you describe: those two adjustments with other setting left default should help. I wish you every success: good luck!!