I want to address some issues before actually sending anything for print. Some colegues mentioned them but I want to summarize.
There are several kinds of files.
In this case, is pretty obvious that you are trying to send a working file. You should not. You must prepare an output file. Normally it has some characteristics depending on the project. Sometimes a good PDF preset and a PDF version will give you a good output file, sometimes you need to take some extra steps.
I. Separate into layers
I always separate my project into layers, the layers that will have raster images at the bottom and the ones that should remain as vectors, like text and logos at the top.
This allows me to make a quick extra step just before sending the files to print, this is flattening all the raster layers into a single object. This way, this single object can have all the interactions of colors of the previous objects. Blends, transparency, etc. in a controlled fashion.
I do not overwrite this "flatten file" I rename it first to ProjectName-09-Output.ai (the 09 is the version control) Then I export this AI file into the proper real PDF Output file. This extra AI file is just for some especially complex projects.
II. The proper resolution
Send whatever needs to be sent as vectors but the bulk of the file size will be humungous raster images. The previous step will prepare the road to make this one. You can simply resample your raster image to the proper resolution. This issue has been talked about many times. In my opinion, a raster image of about 6000 to 12000 pixels in its larger side is enough for any printed size.
The previous steps will give you a really decent output file. You can still use an internal JPG compression. Use the maximum values of quality, and will give you a slightly lower file weight than zip compression. This will be less noticeable if your raster image is in CMYK mode.*
IV. You can not send a big file by email
What you do is upload the big file to some kind of service and send the link.
You can have a hosting provider and upload the file via FTP on your own webpage.
Use something like send.firefox.com or YouSendIt, WeTransfer, GoogleDrive, etc.
*I am not addressing other things like color mode or embedding fonts...