Ya it can be done even with small companies. 
And yes e-verification is not required for H1B. It is required only for STEM extension. 

Since there are only 4-5 employyes, it is better if there are no other h1b employees..so check that. If 50% or more are under h1b, it's considered h1 dependent company and needs to provide additional documentation. So check if there are any employees with h1b. If all others are US citizens or residents, its good for u. 

All they need to do is offer you the salary equal to or greater than the minimum prevailing wage for your responsibility which will be obtained once lawyer files prevailing wage application during the process

So get a good lawyer, the lawyer will handle everything. You or your company doesn't need to know everything about the process. All you and your company need to do is provide the information and fees the lawyer asks for.

So just make sure you have decent salary and you job is relevant to your field of study. 
Good luck..