It's always best to call I think.
When advertising a horse I got a lot of emails and when they made appointments to come and see the horse they wouldn't show up. There would also just be a lot of back and forth with questions that could have been done so much quicker over the phone.
I think if you're serious about a horse the best thing to do is call up straight away.
I don't think in general its good to send videos of you riding to people (no offence) mostly because they're probably not that interested, especially if they haven't even replied. They probably get a lot of horse crazy kids responding (I always get those emails) and I think are more likely to just disregard it if you send a video and all info about your self. Most people just don't care, if they care they'll ask. They'll see you riding when you come out to see the horse. They'll ask all the questions they want when you come see the horse. No one wants an email from a stranger with everything about them.
Otherwise remember you're the one buying the horse - you're not trying to sell yourself as an owner! Keep the upper hand. So many sellers seem to try to twist it as if they're doing you a favour selling you their horse, and it makes the horse seem better than it is. You're the customer. You have all the power, don't just give that away by trying to convince the sellers you're a good owner.