Having wizards and not training and using them is like having an armory full of muskets and not bothering to keep powder and shot. I think #1 is off the table that fast, if the military knows they have a large number
They will be weaponized, just like people always do in D&D type games. No one packs theurgic spells, only thaumaturgy that will increase the local entropy quotient!
Now, a great deal depends on what your wizardry is and can do. Maybe it's all informational type magic, but no fireballs and lightning bolts. You didn't tell us what "wizardry" is in your world.
I will suggest that you grade ability, so you do not have one regiment of three that are fireball spitters, as this will seriously imbalance challenging characters and make your plot-building difficult. That is, even when trained, most people start out with lower abilities, or different abilities, and it's a rare talent that can play human flame-thrower.
Of possibilities 2 & 3, it depends on how wizardry works. Can wizards be integrated in units, or is there something about mundanes that gets in their way? It's how you want to build it (me, I want weather wizards in my navy).
A problem also comes up with "a military similar in structure to the modern US or ancient Rome" in that those are two fairly different things. But I do take away that you're talking about a soldier army, not a warrior/hero/knightly kind of thing, despite the "medieval setting" (classic herofy tech level & costume & culture, I assume, w/o feudalism). A Roman army (or Chinese armies in most eras) had separate units of slingers, archers, mounted javelineers, crossbowmen, clibinarii, and so on, kept separate from the infantry phalanx of the regular legionaires. A modern army has high integration: in the 20th C every unit has its radiomen, one BAR for every so many regular riflemen, a certain number of scouts, and so on. That could be your telepathic wizards and the one who does fire rain or static crackle (if you've ever gotten doubled up by a good static jolt, don't underestimate it as a weapon) while his buddies use their spears, and the wizards who can magically locate things or far-see are the scouts.
Separation of units often had more to do with use (cavalry units do a whole different thing than infantry, and armored trench-attack units in WW1 only worked if they were a group that hit at once), sourcing (all your slingers come from Rhodes, and your archers from Crete, and firepower is better massed), or training and equipment (flame-throwers tended to be grouped, though one guy with the flame-thrower is supported by thirty regular guys, because flame-throwers needed all the same supplies to refill their tanks).
I'm also going to suggest that if magic is a thing, you are more likely to have female auxiliaries in that line. Human "radios" are too damned valuable to waste good ones! They are not likely to be in the front-line units but back in the command units. They may also be in home-defense units, if no one wants little Miss Lightning Bolt in the frontal assault. She sure would keep down the number of siege ladders on her part of the city wall.
Hope that helped!