Welcome to the forums and the soon-to-be ever exciting world of budgie ownership!
You have certainly come to the right place as you will find all you need to know on budgie care here.
The information on the several articles and sticky threads at the top of each section of the forums will be extremely useful and of benefit to you and your budgie friend(s).
Given the schedules you have presented, not to mention all of the extra time taken in tending to your baby, getting two budgies (preferably two males to prevent any potential problems with eggs) would be the best choice.
With the right approach and by dedicating some time for the proper bonding to be established and developed, it's possible to tame two budgies who share the same cage.
It's not realistic to assume the budgies will choose their favourite human companion over the bond and deeper friendship shared by a same species mate, but it's still possible to make a good connection, work on establishing the foundations of trust, solidify the bond and reach a decent level of tameness.
You can even take advantage on the budgie showing more receptiveness towards you and work more closely with him/her to later on make the taming process and the earning of trust easier for the shyest budgie (even though the budgies are housed together, individual taming sessions can also be done, it doesn't necessarily have to be with the two of them at all times).
Best of luck with your decision!