The starter companies are recommended because they provide good instructions, are more accustomed to dealing with shoppers who have not yet figured out what they are doing and they have nationwide clients so can provide shops anywhere in the country that there is a gas station of a fast food joint.
You probably won't hear anything until Monday or Tuesday because many companies were closed for the holiday weekend either including Friday or half way through Friday.
How long to stay with the starter companies depends on how comfortable you are doing shops. There is little reason to spend the time sitting down and signing up with all of the 200+ companies listed here and looking for work until you have some notion about whether shopping is something that you are comfortable doing and having some success with. And to this day I am still shopping with one of my starter companies--not because they pay well, but rather because they have a couple of clients I like that pay okay, the shops are simple enough to be 'almost throwaways' and the company is reliable about getting payments into my checking account by direct deposit.
A reasonable approach is to start a list of companies you have signed up with--whether you have been accepted or not--with the date you applied. Jobslinger.com can let you know what companies have recently had work in your area, so those would be the sensible ones to sign up with next. Discussion of various companies will give you ideas of what companies to sign up with after the ones from Jobslinger and over time, you can fill in the gaps between your list of ones where you have applied and a list of legitimate companies such as on this forum. Because you are likely to end up signing up with 100 to 200 companies, I would encourage you to make your list in Excel or on loose sheets or something that can be easily alphabetized to help you find if you are signed up with a company.
Once you are accepted by a company, I would encourage you to bookmark their login page. My personal preference is to use Firefox because I find their bookmarks intuitive both for creation, for organizing and for Firefox to keep track of my passwords. Of course login and password are also recorded on my list of companies so if something goes awry with the computer I will still have them and just have Firefox remember them all over again.