First of all, welcome to the site. Second of all, you need to decide what your long term goals are regarding this business as it can effect your equipment choices. Are you simply wanting to mow a few lawns on the side for extra pocket money, or is your goal to gradually build into a serious business? If it is the former, a light duty trailer and low-end commercial or high-end consumer equipment will get you by. If it is the latter, you will want to purchase equipment that will stand the abuse of increased usage.
As for the time you have to devote to the business, you have to do, what you have to do. Most of us started part-time, and many on this site still are. What are the hours of your day job? Is it possible to mow before or after work? The worst problem with having only certain days you can mow is the weather. For example, if you can't mow on Monday or Tuesday at all, and you get rained out the weekend, then you are immediately in a bind. Throw in a lot of rain and heavy spring growth, and you will have upset customers in a hurry.
My advice is to grow slowly, and not bite off more than you can chew. Speading yourself too thin is a sure recipe for disaster. Good luck.
Dependable Mowing Service