So, I'm starting a new job soon. One of the things they require of me is to send them via email a password so they can create a company email account for me to use.
I don't feel comfortable with this because
1) sending a password via email is potentially asking for trouble
2) I don't feel comfortable with a company spying on me. I understand that the emails I send will be company emails, but I feel privacy should be respected.
You're right on 1), but in practice the odds of someone other than a government grabbing it en route are fairly low, and the government probably isn't interested in your work email password. The bigger problem here is that if someone else in the company has your password, they can log in as you, and take nefarious actions while leaving your digital fingerprints behind. Once you're more established in the company, you might try pointing out that as long as passwords aren't kept private, any digital audit trails the company keeps aren't going to be on solid legal ground if there's a problem.
On 2), I'm afraid you don't have a leg to stand on. Any emails you send on the company's system are the company's property, which they have every right to look at. Assume they do, and use your work email only for company business, never for personal messages.
Technically, there's a strong chance that your employment agreements even give the company ownership of your personal emails, if you write them using a company computer, regardless of what email service you use. I haven't seen a company try to enforce that, but be warned that companies often do install their own security certificates in any web browsers on their machines. These give them the ability to spy on and record even encrypted (https) web sessions. I always install my own copy of Firefox, and use that if I want to check my personal mail, or do any shopping or banking from work.
There are usually some other surprises hidden in the fine print of employment agreements. Feel free to post them here if you can; it's often interesting to compare them.