Homeschooling Moms
Replies

Oh that's a hard one. I don't know that there is a "best." I think that each individual child will have one that works better for them. So it would probably be best to decide which one you think is best for your child.
My sons are using Math U See this upcoming school year. Basically I think that this curriculum will be great for them. I have also heard raving reviews about it. The other reason I chose this one is because the subject matters are taught thoroughly before moving on to the net material. 
We use Saxon. I've come to the conclusion that if you want your child to hate math then choose Saxon. It is a very good curriculum, but it is dry and the kids hate it after a while. But we are sticking with it because we want their math skills to be excellent.
I have heard that Singapore is even better, in terms of student achievement, but I have not taken the time to look at it. 
It really depends upon the child. We've used Saxon  although not for a 4 yr old, to the extent there has been an overall plan, we start with Abeka and then move to Saxon for upper grades. I've never used Math U See, but with our youngest who turned 6 in December, I wasn't completely satisfied with Abeka  it seemed a bit too easy for him, so we moved to Singapore (Level 2 A) in the last couple of months. The jury is still out, but it seems to be a bit more challenging.
The differences that I see: Abeka is big on review and repetition at the younger levels. You do need to have the "math races," as we call them, books, to work on addition and subtraction combinations (for first grade). I suppose you could also do flash cards or get the combination pages off the internet, but it's very convenient to have the combinations that he's been studying available without having to think about it.
Based on my experience with Saxon at the higher grades, its approach with respect to daily repetition of what has already been learned is very similar to Abeka, but it seems to me to jump around a bit more with respect to what is introduced and when. In other words, you start one concept, and then you'll move to several other concept entirely, before returning for "part two" of the first concept. This isn't a bad way of doing things for some kids. My daughter really does well with it. Our middle son, on the other hand, found that he did better if he FULLY understood a concept before moving on to something else, and so we moved him to a more conventional math book (this is for algebra, though).
Singapore takes a more conventional approach. Thus, our youngest son's math book (Level 2A) starts with addition and subtraction, then moves on to multiplication and division, etc. There is still review, but it's not daily. They do have an approach of "showing physically" before moving on to the concept, but it's not a strong as I understand Math U See to be  although, again, I have not used "Math U See."
If I were trying to choose between them, I'd focus on how your child learns. If he or she tends toward the physical and doesn't like to do memorization or "following the steps," I think strongly about Math U See. If they tend to like to try to get the "big picture" and like to do a lot of different things all at once (i.e., they get bored doing 20 addition problems, but are happy if they can do 3 addition, 3 subtraction, a few fractions, etc.) I'd think about Saxon. If they need to really focus on something for a while and "dig deep" in order to feel comfortable, but like to "think it out," I'd go with Singapore.
And remember, if one doesn't work well, you can always switch. Singapore and Abeka, at least, are not super expensive.

I've only used Math U See from your list. My 1st grader only needa help reading the word problems but is able to do her books herself with minimal help. My 4yo ds loves the program as well. He only really plays with the blocks BUT it is setting the stage for him :) I love how MUS is more self paced. I can add supplements as needed or we can speed through anything that is too simplistic.