I'll start with the round pen as that's a shorter answer. Most average panels that you buy at farm supply stores are either 5 or 5.5 feet tall. That will work fine for broke horses who just need a refresher.
Now, for the ties. Personally, I prefer a single straight tie instead of cross ties, especially for the initial tie training. It seems to give the horse a bit more movement with their head and doesn't seem to be quite as panic inducing for a horse that isn't used to being tied.
As far as what to tie them to, I prefer that they have a fence at whatever they are tied to instead of a solitary post. The fence keeps them from getting wound up around the post if they get nervous. Plus, something like a hitching rail works a lot better if you are handling multiple horses. You don't need as much space as you would if you wanted to have cross ties for each horse.
For post size, I wouldn't go any smaller than 8" diameter (if we're talking wood, if you choose metal, you can go smaller) set about 4 feet in the ground, and set in concrete. The last thing you want is the post leaning/coming out of the ground if a horse decides to fight.
You'll need the tie ring to be tall enough that they are tied at or above wither level. If the tie is low, they run a greater risk of being injured if they fight.
Just as an example, this is where I tie when I need to have it tie solid and hold up to anything that a horse can dish out.