The new partner wants to buy into our business. Now since we're selling him company shares, we're not sure whether we need to receive the money to our personal account OR invest it into the business! Is there any general rule here?
Depends on type of business entity you're using.
If it's a sole proprietorship, you can do anything you like.
If it's any other form, receiving money personally will nullify your business. Read up on mingling personal + business money.
And as always, this is a question for you tax preparer.
To be safe, just receive the money as if someone made a payment for goods + services to your business... so... person would write the check, just as if they were buying from your business.