Fresh is more effective than frozen, but frozen will work just fine for most people. IVF is more effective than IUI, but much more expensive and invasive, so most people try IUI for at least 3 cycles first. Known donors (a friend or someone off the Internet) works for some people and is way cheaper, but there are a lot of issues to consider. It seems to work out fine most of the time, but if it goes wrong, it can go very wrong. There have been cases where women have sued donors for maintenance, or donors have sued for visitation, so you need to check the law in your state.

I don't think permanently anonymous donors should even be considered. Some donor-conceived people could care less about their donor, but for some, it's a huge huge deal, and they are very unhappy and in some cases angry about not being to find out who he is. I wouldn't want to have to explain to my own children that there's no way for them ever to find out who their genetic father is. In some countries, donors have to be ID-release, or they simply can't be donors. I think it's likely that everywhere will be like that by the time your children grow up.