The first mistake will be to start a digital marketing agency. (WAIT : Do not jump to a conclusion as yet, please read on ......).
Things have changed and now keep changing even faster in the world of digital marketing. In other words, now, digital marketing is very deep and very wide and keeps getting deeper and wider day by day. Instead, you must ideally choose 1 or 2 specialities WITHIN digital marketing and offer those specific 1 or 2 services, otherwise you would be a jack of all trades and master of none, considering how wide and deep digital marketing has got now.
For example (JUST AN EXAMPLE ONLY), you may choose to offer content writing & graphic (logo, banner, etc) designing. Each speciality within digital marketing nowadays has great demand, but you will have to be great in marketing and also in selling of your service(s). And ofcourse, as your business grows, you may then consider adding more specialities within digital marketing, into your business's "operations".
The above is my perspective about going about to start a business which relates to digital marketing and ofcourse different people would have various different perspectives.