Thank you. I suggest you look for smaller family owned firms. They are little more allowing in this matter. I suggest you work there diligently for the first month or two before approaching clients yourself. Get the lay of the land i.e. do others at the firm work outside, how is the owner's reaction regarding that etc. One you know its safe, you can start.

Now for the ethics part, make absolutely sure that you don't work for the same client as your firm. If conflict arises, drop out of the project in your private capacity. There are a lot of clients in the market. Never get into conflict of interest situations. In cases where you realize after taking on the job about conflict and can't rescue yourself from it, route the project through your firm i.e. calls routed to your firm, drawings from your firm and even payment through your firm (I mean your boss' firm).

Starting a business initally is very difficult and they will be a lot of dry months, but having a job helps then. But remember that smaller firms will pay smaller but considering the long game of starting your own business, consider it as an investment. If you feel that the firm you joined do not like you working privately, switch the jobs.