When you move to a new country, it is unavoidable to dig into your savings in order to pay for the moving costs, arrange housing and allow for some time to look for a job.
Of course it would be better if you already have a job lined up before you move. Have you searched for jobs? Why have you chosen Ontario? I think it would be a good idea to keep an open mind about which province to move to while you check your job opportunities. You can apply from where you are and set up interviews. Then go on short trips to do them. If you have high demand skills, you may even find an employer who is ready to help you with your moving costs.
For your child, you would be eligible for UCCB (Universal Child Care Benefit) which is $100 a month for each child under the age of 6 and CCTB (Canada Child Tax Benefit) which is $120.50 if your income is less than $25,000 a year but starts to get cut after that. As you are new in Canada, they will use your world income in the last 2 years to calculate. There is also NCBS (National Child Benefit Supplement) which is however only paid to low income families so you may not qualify for that. If you make less than 25,000 per year, you would get $186 per month.
Your wife can get EI maternity payments only if she manages to work 600 insurable hours in Canada before the baby is born. You are not eligible for EI unemployment benefits if you don't find a job because you would also need a certain number of hours worked before you would qualify.
As for health care, some provinces have a waiting time for newcomers before they get coverage, for example in Ontario you get coverage 3 months after you move and in BC 2-3 months (1st day of the 3rd month after your move). During the waiting period, you would have to pay your health care expenses out of pocket. Quebec has a 3 month waiting period with an exception for pregnancy and childbirth. Other provinces mostly give you first day coverage if you are moving from another country. However, most provinces also have an eligibility clause where you must commit to living in the province 6 months a year to be considered eligible. It has happened in some cases that people who have lived in a province for less than 6 months and then moved have been back charged by health care for the expenses they caused as they have been deemed not to have fulfilled their eligibility clause. Having a baby in Canada can cost thousands of $ so it is important to make sure you are covered and that you continue to be eligible to be covered. After more than 6 months in one province, you could move to another province and your old province health care will cover you while you wait for coverage in your new province.
If you choose for your child to be born in the US, you would have to sponsor him or her for PR if you decide to settle in Canada. As a PR, you are allowed to live outside Canada for up to 1094 days in your first 5 years as a PR and in any 5 year period after that so that is up to 3 years you can stay outside before you have to decide.