I show a lot and in the UK that means conformation is king so:
1) is always conformation. If a (mature) horse has visable flaws in the photos I am sent then I don't even bother looking at it further (youngstock is a bit different as they can mature and change shape)
2) Temprement - I like my horses to be nice people, to be a pleasure to be around, to give kisses and cuddles, to be intellegent and willing to learn and to be flexile.
3) I look at type - what class would he fit in? If he has no perticular class then realy he is no good for me.
4) I don't like doing the basic handling myself as there is a high possibility of othe the horse and I getting hurt (and a scar on a horse can end a showing career) so will never go for something completly unhandled. At a minimum it must happily wear a headcollar and lead in a fairly sane manner!