I find it incredibly stressful to try and work while simultaneously looking after children, can't recommend it - I found I did neither well and just felt anxious all the time. HOWEVER. Being self-employed as a mum has worked well. I would recommend starting some kind of self-employed work alongside employed work before having your child, as you have more time and can learn the ropes before you actually need the income.
I do consultancy, selling the skills and knowledge I built up in the first 10 years of my career when I was employed. People who want advice and expertise in my field will bring me in for a day or sometimes as little as an hour to train and advise their organisation. I had the advantages of some savings to live off while I worked out what I was doing and how to find business, the first year I got work through my contacts and then I spent about £1,500 on a website, branding, photos and copywriting to produce the information to sell my services - this was well worth it as it helped me work with people I didn't know.
The big advantage of this type of business is that it is pre-booked (so I can pick my own hours) and this means when I'm not booked, I don't have to think about work. I can hire a baby sitter at short notice for the day or the hour that I need them, or ask family to babysit so I can work. This meant I could return to work 2 months after having a baby because some weeks I was only doing 2 mornings work, or just worked in nap time to do a report or a phone call. The work is highly paid, so I could do something that would take me, say, 2 hours, and earn £100-200 from home - that might be my only booking for the week, at times, but I wanted the time-flexibility so I could look after my baby everyday. If I'd been working on a day rate or had a shop or something I would have had to have regular childcare and would have been harder with a non-sleeping breastfed baby.
The downside of it is, that it can be lonely. You need to be self-motivated, and you probably need to have a bit of savings to manage during the times when work is slow or if you have to buy something you need for the business. Being self-employed has made me the main carer, so there have been times when I've struggled to keep work going alongside school holidays, and organising the ad-hoc childcare is a job in itself.
So my advice is:
Invest in developing your skills and experience while you are employed/studying.
Build your network up as much as you can, so that you have a contacts book to call on when you start your business.
Think about ideas you are interested in trying, don't be afraid to try and fail and move onto something else.
If possible, do this before you have kids - but failing that if you were employed pre-kids, maternity leave is a time lots of people try setting up a business as they have some maternity pay and you are allowed to do self-employed work while on mat leave. However I think its hard to get it up, running, and working well in that time frame and decisions about going back to work come round quickly.