From reading through the Singapore site and using the books, I think to get full advantage of the Singapore program they recommend that you use the Textbook, Workbook and then the Challenging Word Problems and/or the Intensive practice (I think they suggest "and" rather than "or"). For the younger years, though, I used just the Text, Workbook, and Extra Practice. We started the CWP later.
The Home Instructor's Guide came about as a response to the overwhelming homeschool use. It is written to the parent and gives teaching tips, etc., as well as the answers and a rough schedule of when to do what. The Teacher's Guide is what they had prior to the HIG and is written more for classroom use. I found the HIG more useful in the later years. For 1 and even 2 it is pretty easy math and not hard to correct yourself. You may want it for extra activity suggestions. The guides are optional, though.
The US Edition includes standard measurement (not just metric) and US money. The standard edition is written for students in Singapore and doesn't include those. I would recommend the US edition.
I have not used Horizons, but I think starting at 1A would be best because Singaore teaches the kids to look at math problems in a different manner than most US programs.
I have used Singapore 1 - 3 with all of my kids and they really liked it. My ds is using Singapore 1A now and loves it. He is young, though, so we are only doing the workbook. He did the Singaore K program and wanted to continue.
HTH!