you have to have the money it costs, you have to have enough to buy proper tack (most saddles are $500+), you have to have a savings account with at least $500 for vet bills. our farrier costs $45 per horse, both are barefoot. hay costs about $4/bale, you need at least 100 per horse. if you're boarding, you need board set for at least a couple months.
Not including the money to buy the horse, I would say around $1000. Just to be safe. You need to buy the food and get a vet check. Barefoot does mean more frequent visits from the farrier. So depending on how much your regular farrier charges. Per week..not much if anything at all. I would think of it as per month. Not per week. Per month, say you get your horses feet trimmed two times a month, that would be maybe around $100. It all really depends on the horse haha. Hard question to answer..haha
I think it depends on the country where you live, but I always tell clients to save up for at least 3 months of livery costs and set the money aside. Also you would need money to buy a fitting saddle, bridle, bit, rugs and other extras if those aren't sold with the horse. I personally spend about € 80,00-90,00 a week for my horse in the Netherlands. This includes farrier, half service (includes feeding and mucking out) livery and small extras. I have €1000 saved for unexpected bills such as the vet, replace a damaged saddle and so on.