I guess I don’t know what you mean by systematically? If you live in the US your parish should have a Religious Education program in place. You could always be more involved in this yourself starting right now. I am fortunate enough to homeschool my kids and because we use a thorough Catholic curriculum, and because out priest is supportive of us we do not currently use the Parish RE program for sacrament prep. But we have in the past and it has been more than adequate. Some parishes require this some do not. This does depend on the parish though and if there is a problem in your current parish, it is better you know it now so you can either attend a different parish or volunteer to help change the quality of the program.
That being said, parents are the primary educators of the faith to the children, so in no way should you “hand off” your kids to the parish and walk away.
Buying a Catechism and having them memorize it would not be advised. However the Baltimore Catechism can be used for this, as it was written for such. There are plenty of good resources out there. Try Seton, or Ignatius Press.
If a three year old says the Our Father, Hail Mary, and Glory Be. And can pray at meals then you are ahead of the curve.
Remember, their brains can easily memorize but cannot comprehend certain theological ideas and concepts. Rote memorization on what the council of Nicea was and the immaculate conception will impress the neighbors, but will mean nothing to a young child.