I have a Quarter Horse and an Arabian. While I love them both, I definitely wouldn't recommend my particular Arab for beginners. I've also ridden Morgans, Appaloosas, Thoroughbreds, Paints, and grades. QH is still my recommendation for beginners.
As far as height is concerned, there are a lot of QH out there that are tall.
Do you have someone who can help you in your search? It's a very good idea to bring an experienced horseperson with when looking at prospective horses.
As far as websites to search on, in addition to equine.com, I've also searched on www.dreamhorse.com, www.equinenow.com, and www.horsetopia.com If you type in "Horses for Sale" in a Google search, you'll come up with a ton of results. Also, I see you're in Wisconsin so you might want to check www.horsesmidwest.com. Be careful of that one, though. There are a few horse traders on there that are a bit shady. They are only interested in profit and not the well being of the horse, so they have no hesitation in selling you a horse that isn't suitable for you or a horse that is lame or extremely old (all the while passing it off as a sound horse). If you click on "List all Horse Ads for this Seller" and get a ton of results, with many different kinds of horses for sale at extremely low prices, you might want to be careful with that seller. If something seems too good to be true, it usually is.
Hope this helps, and welcome to the forum!