I researched at home insemination a few months back, as I had to have vulval surgery for cancer so for my OH and I, intercourse was not an option, and there are various non-dangerous methods.
One of the easiest is to use softcups, with a little pressed. Your donor places his sperm directly into a new, and therefore sterile softcup, and you place it inside you for up to 8 hours. You would benefit from a few minutes lay down with your butt on a pillow, and would benefit even more from an orgasm.
Otherwise you could use a sterile syringe to place the sperm directly at the wntrance to the cervix. As long as you expel air, there is no danger. Again preseed could help things flow a little, and a littel saline in teh syringe can help the consistency. Again follow this by lying down on cushions and an orgasm.
I see no reason to pay anything for donor insemination if you are both healthy.