First let me say Yes I think you can do all three of these programs. LHTH is very short and Preparing is adding a lot of independent work and you could even go heavier on the independent side. So I think that is very doable. I am doing LHFHG and BHFHG and one of my children has special needs and requires a lot of extra time. I feel like I could easily add LHTH to my mix and still have sanity so I think you would definitely be good with those three.
What you need if cash is tight to still have a good program
BEYOND
-ECONOMY PACKAGE (Necessary Items) need these no negotiating
-BASIC PACKAGE (Necessary items, unless you have these areas covered in some other way, or you need to economize.) To me these are very necessary unless you are doing Math or Science in another way but I would go with the CD and the devotional they add a lot but this is a section you can skip if you really had to skip something. If you did not do the Science and Math you need to cover those topics in some other way. I would consider at least the devotional book because it is so good.
-DELUXE PACKAGE This comes under the heading of awesome to have but if things are tight this is what you are going to skip. If you wanted to do these though you would be picking just one.
-What you will also need for your Beyond level kids.
The Emerging Readers when your dd finishes phonics and you will see those in the yellow section on the right.
Your independent reading child in Beyond will need DITHR or some other reading program. I really recommend getting DITHR especially for the large family. Here is the reason, the Teacher guide is used for all levels then you have student books that cover two levels and are reproduceable so you can use them again and again with the next kid ready for that level and here is the big one...you can read any books you want so the library is your friend. When you look at the value it is a very economical program. If you decide to do that you need level 2/3 in the student book and whatever levels your other kids might hit. OR you use your own reading program of your choice.
Little Hands To Heaven
The first box you either pick one of the Story Bibles or pick your own (hers are awesome and listed by age appropriate)
Second box- Pick one devotional
Music- need that
Teacher Manual have to have it.
Preparing
-ECONOMY PACKAGE need all of this
-Science Adder to Economy Package need this only if you plan on doing science at the Preparing level or use your own and bump it up for an older child.
-BASIC PACKAGE these are the read alouds. They really add a lot to the program but if money is tight you have to make the call on these.
-SELF-STUDY EXTENSION PACKAGE FOR OLDER STUDENTS I think you would not want to skip these. But here is where I would really ask Carrie on what she would suggest if you could only get either the Basic Package or the Self Study Extension. It would be a really hard call for me and I am not sure what is best in that case so I do not want to take you down the wrong path.
-DITHR 6-7-8 student book and the same Teacher book can be used from DITHR here as I listed in the Beyond section. So you see one TM and you buy two student books and get five reading levels you can use again and again with any books you want.
But anyway that gives you some numbers to crunch. Look at the packages and read what she has listed after them in terms of economizing.
HTH
I am interested in what to use for 3 of my little ones. I am considering LHTH for my 2 year old (3 in November) because it looks like SOOOOO much fun! 
So, if the budget doesn't allow for all at once. . .any suggestions on what to start with and what to add later?? Appreciate the help 
We are LOVING it! I can't wait to hear what you decide...., Mary