So, first let me say that I am not advising for or against home birth for you. I think every woman, pregnancy, and labor/delivery are their own entities, and I'll just tell you my experience.
I did choose a home birth. It went well, medically uneventful. I want to note that I did choose a midwifery team which had good hospital connections and who were very clear about their criteria for transferring. This was important to me, because if we had transferred, they would have been able to attend as doulas.
Housecleaning was not a big deal. I keep a fairly tidy house and did a deep clean on the things that needed it in the week before I was due. My son was born in his room and I made the bed twice, so that we could have the baby and afterward, any soiled sheets could be easily stripped (just use a shower curtain or waterproof sheet between the two sets of bedding).
I did attend a great birthing class which focused on being present through the labor and birth itself, and being open to all the possibilities: natural birth, birth with interventions, and cesarean birth. I appreciated the fact that the midwives took time to prepare us well for any eventuality.
We rented a birthing pool, which I never got into. Not a toe. Baby was coming too quickly when he was finally ready.
What I liked so much about birthing my son at home is that I'm a fairly private person, and I liked already knowing who the attendants were and being in my own home. My husband and I were alone most of the time (in about 1.5 hours I went from 'relaxed, mild labor' to "transition/wanting to push"). I believe that with a home birth, you really need to have support which is grounded and centered. My husband was able to do that for me.
One thing to consider is simply "Do you want to do this at home with three kids around?" Consider your child care arrangements, and then, make back-up plans. Will you have options available if you happen to go into labor while one or more of your children are sick? While I had my own son at home, if were were to have had a second, I would likely have had arrangements for him to be elsewhere. For some children, witnessing mother laboring can be upsetting. There are their feelings to be considered, as well as your own. It may be hard for the kids to be in the same house and leave you alone if you need quiet or privacy.
Lastly, go forward in your pregnancy with an open mind. There are sometimes developments which would suggest that a hospital birth might be the better choice. I kept an open mind about that, and was glad I did. Had my son been presenting breech or had there been other concerns, my plans would have changed quickly. Also, since finances are concerned, do some serious talking with the midwife. Can she attend if you do end up transferring? Is there a different rate of payment if you cannot birth at home or the center? My understanding is that then, you may be financially on the hook for both the midwife and the hospital, and maybe the midwife will reduce the fee if she is allowed to attend as a doula.
Lots of stuff to think about. I hope your birth experience--no matter where it takes place--is a good one for you and your entire family.