I have had this discussion with some people on the GG forum, and opinions are divided. Goats are at their most fertile as goatlings, so should be higher chance of success, but you are starting from a lower success threshold.... I think it depends on how good the inseminator is, and you getting your timing absolutely right. I decided to go down the natural route with mine, although it does involve some travelling (and in the case of my goatling a return journey three weeks later, as she didn't hold first time round). I also do not have anyone near me that could do AI for goats, however it is something that i will investigate further in the coming years, as some really good GG semen is now available.
I have had my goats sponged now for two years in a row, and it works very well. You can discuss your timings with the billy owner in advance, plan to take time off for travelling or arrange boarding.
It also depends on what your aims are with breeding your goats. If you just want milk for the household, then the actual breed/pedigree of the billy is not so critical, but I try and breed for milk, so go for pedigree/high milk figures billies (for my BT's, and to a lesser extent for my GG's)