Is it even worth it to do "professional" web design on the side? Will anyone take you seriously when you can only work part time at night and on weekends? How can they when if they want you during the day they have to call you on your "real" job?

Who knows I guess. I am starting up a web site to show my web skills and allow people to request my services. I am just a bit worried about the amount of time I can actually invest in these customers. What route should I take on the site? Creating a business/company feel? Or go straight honest and have the site note that its a part time thing from one guy? I've only done things for friends and family in the past so my business experience is slim to none. However, I do not want to ignore what I think I am good at.

I'd say it's a waste of effort on your part.

Not only can you not attract serious customers who can pay (you may get some kids wanting a l33t kewl design for their personal homepage for $5 or so) because you won't be working at times you can communicate with them but the competition of serious professional design firms is extremely fierce.

Best you can do is probably to make a site showing your skills and use that in combination with a well written resume and cover letter to look for a job in an established web design firm (or department in a larger firm).

If you already do it as a job you should be even more careful as working in the same field on the side (as you plan to do) is very likely not allowed under your contract.