wow this is my first time in this section! what a beautiful horse!

Does your mare have documented breeding? If so I would also look at her ancestors a few generations back as if there is a large amount of variation in them, it decreases the likelihood of the offspring having a similar phenotype to the dam or sire - e.g. you could get a throwback from the shire.

You need to think about how marketable the offspring will be. If you are thinking of breeding for yourself, you still need to bear in mind the market because no future for any horse is guaranteed and you may get to a point in the future where financial needs must and you need to sell. At this point you need your horse to be in some way marketable - this will, of course, also be down to your skills in handling and bringing up your youngster.

As you said you want to produce a SJ/event type, does your mare have any kind of record in affilliated eventing or showjumping? If yes, you need to (as another poster said also) absolutely tear apart her conformation, movement and jump and find a stallion who is strong in all her weak points. If no, I would question how you would expect your mare to produce an eventer or showjumper if she has no proven record in either.

Also, especially for a sports horse type, if the stallion isn't graded, forget it. Consider getting your mare graded too if you are serious, it will give you an expert's opinion on her and what stallion she is best suited to. With a lot of stallions now, they will be available via AI so I wouldn't worry too much if the stallion isn't near you or even in the same country as you!

Go on to SHBGB and the AES websites for more info on sport horse stallions.