I know a bit about this as I have three dc conceived with donor sperm (DH has zero sperm count caused by genetic fault)! Our first dd was conceived in Jan 2005, which makes us a bit different from people using donor sperm now as our donor is and will remain anonymous. The rules allowed us to save samples so that our other children have the same donor, so they'll all be in the same boat.
Re choosing donor-we had some choice but not loads which, in a funny way, made it easier. Had I had full cv, photos, etc it would have been hugely difficult. As it was, we chose same hair colour as dc and roughly same height (DH is very tall). Blood group less important for us because we intended to be and have been (from very tiny, but discussions have become more sophisticated as they've got older) open about how they were conceived, although fairly private with everyone else (close family and friends know-it's not a secret but hardly a coffee morning acquaintance chat!).
I can honestly say that of all the challenges parenting has thrown up, the DC issue has been nothing at all. The children are not all that interested, although DD1 decided that the usual way of conception is so disgusting that she intends to use a donor. I had to break it to her that that isn't how it works!
We were lucky, as I fell pregnant easily with donor sperm and so we never went further than unmediated IUI. I did have miscarriages when trying for DS (DC2). Generally though, once we got everything sorted with donor etc, the clinic were amazing and we feel extraordinarily lucky.
Donor parenting is, as fat as I can tell, indistinguishable from anyone else's. There haven't been constant questions about donors yet, DD2 (6) knows there was a "donut" involved, which pleases her greatly. It may get tougher when DD1 and the others get into teens and beyond, but the general advice seems to be that children get to grips with it extremely easily if there is openness from the start. I told all three of mine when they were less than three months old, to practise the language and feel comfortable and to properly be able to say they've always known.
Sorry not to have anything more dramatic to say! Do PM if you'd like-happy to help with any questions.