When you save a PDF in Illustrator there are some default presets, but if you look to the left there is a category called “Compression”.
I recommend the following as a ballpark for a document that is light enough to send out but still look good for screen or 8x11 printing:
Usually you’ll have a size you want to hit (IE Under 10 mb)
Start at:
Bicubic Downsampling - 300ppi above 450 PPI
Compression JPEG
Quality Max
From there, you can work down to say 150ppi, to high compression. I would avoid going lower than high on the compression scale since you’ll start to get more noticable JPG artifacts.
With that setting you should get a much much smaller file.