I vote: Homeschooling...ok...I'm biased; I've been doing this for 9 years and have a 4 year old and 2 year old pre-schooling right now. At these ages, school is just a natural extension of the things you are doing to prepare for life and it is an amazing time of discovery for a little guy. So much of what I've read shows that mothers are the primary language givers to children. Just by being with you and engaging in activities they are learning what they need to be prepared for whatever school situation they are going to encounter in the future.
Our 1st child was in a wonderful preschool (that is now closed), but we moved across town. I had a new infant, so dad dropped her off on the way to work. Just as I put the baby down for a nap, I had to scoop him up and go pick up big sister. It was very disruptive to our day. If she stayed full day, the majority of the afternoon was nap (I was paying for her to sleep while I was home and she could nap in her own bed?)
It is good to give as much time as possible doing things at home. There is so much more at this age to have a child develop in than what is "taught" at a school.
If you are already thinking a private preschool then you might find that a good home investment for your money might be a curriculum from Sonlight. They have a Preschool curriculum for 3 year olds that is filled with rich literature and a guide that suggests activities. We've bought many of their "Core" sets of books and love them! (note, we have not been given anything to recommend them, just think they have some of the best selections out there)www.sonlight.com Look for CORE P3/P4
Kumon has some wonderful activity books for doing things like practicing cutting and gluing skills, etc. And they are fairly inexpensive.
Also, I saw that you have the use of a caregiver. You might think about handling the "school" activities yourself and letting the caregiver tend to other chores and little baby, so that this is a special time for you and your older child. Our 5th child had problems with having a younger sibling (the others didn't have as profound a problem) and this time became the glue that said mommy really still cares for me. It doesn't take a lot of time to do, but its rewards are wonderful :)
Also, don't think that you need to home school in isolation. There are many folks with children this age hanging out at parks and doing field trips and activities. Check out www.smoothingtheway.org or look for information on Starting the Way, a support group for 1st year home schoolers that also does a seminar for parents of preschool aged children.
I just read the comment about being social...at this age I question how important it is to learn to be social from a group of 3 year olds and a teacher who may or may not share my family's values. With our first (and only) preschooler, we loved the teacher and all that the school was about (she went at the age of 4). Folks can have wonderful experiences, but I think there are more ways to be "properly socialized" than by peers at school.