My situation was a bit different to yours but maybe you'll find it reassuring - admittedly it never went into practice as I lost my baby early on.
I'm disabled and not working, my partner is also disabled. We have a small income but with good budgeting we are comfortable - even able to regularly save.
We worked out how much we could set aside each month in advance of the baby arriving. We then listed what we would need before baby's arrival - having a costed list is something I found very helpful. We also scouted out where we could save money in advance, and you might find that helpful as well.
eBay is great for picking up second hand baby things very cheap, especially clothes and toys, which you can often buy in bulk. Check out Freecycle as well - a lot of people give away their old baby things and just because they're free doesn't mean they're junk, normally it just means people want their space back or need to make more space for their growing child!
Don't fall for marketing ploys. A gigantic three wheeler buggy is more or less the same as a nice fold up pram in terms of durability, and the nice fold up is going to make fewer people hate you on the bus or in Starbucks 
as well as cost less. Boiling water in a pan is going to be cheaper than buying a sterilizer if you need to use bottles - obviously be safe and make sure your bottles aren't going to melt!
We costed how much formula would cost on the off chance I couldn't breastfeed, just in case, and worked that into our weekly budget. We also looked into nappies and discovered it wouldn't be too hard to opt for reusables and it would save a HUGE amount of money - google The Nappy Lady, she has some videos showing how to use reusables as well as the process of cleaning them, which is easier than I thought it would be.
See if you can develop a budgeting system now. Think about your outgoings and whether or not you can cut down. A good example is things like mobile phones - some people are paying maybe twenty or thirty pounds a month because they haven't shopped around or changed their contract, that could come down to around twelve pounds for the same useage with some companies, depending on available deals!
I'd always plug moneysavingexpert.com as a good source of advice.
And finally, best of luck to you. Don't get overwhelmed. You've worked, you've studied, you're no stranger to making changes to your life. Congratulations!