how should I decide which program to use? For example, if I’m creating a large bulletin board is there any benefit in using indesign? or would illustrator work better?
is there a lot text?
No, but would indesign be helpful because its lighter?
Indesign would be better as text like @shirar mentioned. And the compression in Indesign is much lighter while holding high quality then illustrator or photoshop. Indesign will also give you easier ability to prepare for print. You can always create the illustration in illustrator and paste it into indesign
Just saw you wrote as I was writing, Yes, It would be lighter
So even if I am not really using text, you think I am better off using indesign and pasting in illustrations because it is lighter and for print?
Yes, Even if I would set the whole thing up in illustrator, something like a bulletin board I would always place into Indesign and export from there
With my 8 years of experience this is how I divide up my work:
Vector/Illustrations are done in Illustrator
Photos are done in Photoshop
and then I combine all the work with text, etc. in Indesign to export into whatever format is needed.
I find that although there are links, which I create a “links” folder with each file type, the file is lighter and each part of the file is clear… illustrations/vector work/photos and text.
I don’t know if anyone else has ever done it this way, but this was one way I found the most clear and productive.
I also never had a client come back to me that something was “blurry” or couldn’t be resized, using this method.
You are working 100% correctly 
The “art” should be done in photoshop and illustrator, the final execution/ layout/ etc should be done in indesign