You have to ask when do I want a foal to be born? What facilities do you have for her and the foal. Do you want to be in a tent at the yard in mid January!
Do you want to have a go yourself, do you want to foal her in or outside? Are you going to send her somewhere to be foaled?
Best time really unless you are breeding a racehorse with the climate we have had recently is the month of May as the grass is in for most of her final trimester, which is the best provider to the mare for good quality and quantity of milk and final development of the foal before birth.
So you would be looking to cover around June.
Re Studs
Personal recommendation is always good and an older established stallion with performance and that has foals on the ground is probably better then you can judge what sort of horse he is producing and from what mares, which will give you a good indication of how he and your mare will combine.
I have a t/b 15.2 6 yrs old, was thinking of breeding her with a T/B - I/D. we have all the room she needs and more, don't need a tent LOL, we have house on site. so big plus. looking for a good stud. and here she is. http://i165.photobucket.com/albums/u60/juliefrazzle/100_0192.jpg
with AI you don't need to stick to a local stallion - and many studs will take mares for foaling even if they haven't been covered by one of their stallions
you could look at Catherston - only just over the border from Surrey