You're right to be concerned about staying in touch with visitors. Businesses do well because of the relationships they build.
I recommend that you proceed in three steps:
1) Educate Yourself First. The fact that you’re asking this question leads me to believe that you're not well-versed in online/e-mail marketing. So, you might also want to familiarize yourself with these topics *before* settting up your mailing list. There's definitely a way it should and should not be done. You don't want to risk offending your new contacts. Start with the resources available right here at Entrepreneur.com:
Gail Goodman's Email Marketing column: http://www.entrepreneur.com/columnists/gailgoodman/archive77684.html
And, the Online Marketing channel: http://www.entrepreneur.com/marketing/onlinemarketing/index.html
2) Know the Law. Yes, there are laws. As a budding online marketer, you want to familiarize yourself with the provisions of the CAN-SPAM act: http://www.ftc.gov/bcp/conline/pubs/buspubs/canspam.shtm
3) Select the Appropriate Service Provider. There are many services that will allow you to collect email addresses and manage your list through their software a few I recommend are:
http://www.aweber.com (offers IP address collection for CAN-SPAM compliance and offers many ways to 'slice and dice' your mailing list to run reports on any statistics you would ever need - # of subscribers, dates, split testing, etc.)
http://www.constantcontact.com (to my knowledge does not collect IP addresses for CAN-SPAM compliance but does offer double-opt in)
Take these steps - in this exact order - and you'll be well on your way to e-mail marketing success.