It’s okay if this process feels intimidating. Most graduate students and current professors (including yours) likely wrote a similar email during their undergraduate years. Truthfully, not all professors you write will be so receptive about getting such an email, although an overwhelming majority will be happy to receive this type of email. On the rare occasion that you get a cold/mean response, take it as sign that they would have likely made a poor research advisor for you. Of course, realize that professors are really busy people. It’s okay to politely follow up with an email after a week or so if you have not received a response. But make sure you’re respectful in the follow up. Some professors might take you up on the offer to meet, some will say that they are not taking students. It’s okay if you get rejected during this process. Rejection is a normal outcome of this process. It’s not a reflection of your abilities or potential.