Your regular bills on a safe, sound, sane horse are going to be trimming and shoes approximately every six weeks. In many cases you can only shoe the front, back or none. It really depends on the ground the horse is spending all of their time on and what they will be doing. Your Farrier or an expert horseman in your area is the best source for that info.
You will also have seasonal worming, which is pretty cheap. If you are moving around much at all, or spending time with other horses not from your herd/barn it is also important to vaccinate twice a year.
I'm not familiar with VA. Here in Texas, you have to have a Negative Coggins test to take your horse anywhere. It is a rare disease but it is pretty serious.
Grooming supplies. I like to put Equiflex or a similar product on my horse's hooves about twice a week. It isn't expensive, and keeps her already amazing feet great. She is in a pasture about 12 Horus a day with other horses. I think this combo is worth the results we are getting. Then again, who knows she might have amazing feet without it.
Blankets for winter. A cool weather blanket and a cooling sheet for letting the horse cool off slowly after being worked.
Fly care. I'm not a fan of the really potent fly chemicals, but I do use some of the serious ones during the bad fly seasons only. A horse that is being driven to the brink by dozens of flies is not fun for anybody.
I'd say that is the basic basics. It is somewhat regional. Seek out a really knowledgable horseman in your area and learn whatever you can from them. Horsemanship is like 15% riding, the rest is the care and feeding stuff and being smart with these amazing animals.
Good luck, I think you are about to have a lot of fun when you get back into it.