What stockholder rights should a minority shareholder have in a startup?
Assuming you're comfortable with the percentages, if you want to have any say in how the business is run, do not give up your right to receive voting shares. However, be advised that with only 30 percent, your business partner could easily make all of the decisions without needing to consult with you . . . unless your partnership agreement provides for the issues on which you'll have a vote (usually, having to do with major decisions such as changes in company ownership, company mission or target market, or changes in company status).
In closely held companies, there usually are transfer restrictions because ownership is not traded on the public markets, and you don’t want "just anyone" coming into the mix . . . so those are not surprising. However, make sure that you get the advice and counsel of an attorney to make sure that 1. Your rights and obligations are set out in a partnership agreement and 2. The terms give you some measure of protection.