IMHO there is no good way to watch a child, particularly a child under the age of 5 years old, while working from home. You will not be able to work because taking care of the child will take up all of your time.
For our kids, when they were under age 2, we had a full-time in-home nanny. Yes, they are expensive. Yes, they are considered employees and you will need to pay payroll taxes. You might be able to get away with classifying them as a 1099 contractor, but I would only do that if the nanny agrees and knowing that the IRS may disagree. Our current nanny earns $20/hr plus quarterly bonus. She will also do light housekeeping.
At age two, our kids began attending daycare/preschool. This is much less expensive-- I want to say $1000/mo. Our youngest now still has a day with her nanny, and the remaining days of the work week she is at preschool. She is picked up in the afternoons by her willing grandmas (they split days) and they spoil her for a few hours until we come home from work.
Grandmas do back up child care, nanny is happy to fill in, and the last line in case of emergency is my sister.
Yes, childcare for a young one is expensive. But it is worth it, unless someone wants to be a full-time SAH parent. Also, my kids have really enjoyed their nanny & daycares and, of course, love "grandma time" the most.
We are planning on moving to a different home within a year or so. I'm thinking of looking in to an international au pair, as the new home has a somewhat separate living area. This is because I would like my kids to be exposed to my family's native language more and, they way things are developing now that my kids are older, we could use someone to help with the afterschool & after-school sports pick up-drop off situation