Byzantine might be the way to go.
An
aureus will definitely elude your $400-$500
budget for gold. Then of course the late
Roman Empire has that
denomination problem that Evan and postvmvs state.
Early
Byzantine should give you a nice and large range of coins to collect. However, at the beginning of
Byzantine history you will find silver coinage
rare and even more expensive than gold, once again pushing your budgetary limit. Going into the seventh century, you'll find them more common and hopefully cheaper with the wide array of copper
denominations still in effect. However, by the end of the seventh century the offerings of coppers narrow considerably.
So, perhaps an emperor like
Heraclius (610-641 AD)? Looking through
Sear, that would give you from
Constantinople:
Gold: 2 1/2 Solidi (a special and very
rare ceremonial issue, not meant to be afforded nowadays by us mortals
),
Solidus, Light
Weight Solidus,
Semissis,
TremissisSilver:
Miliarense,
Siliqua,
Half-Siliqua (these three also ceremonial and actually more expensive than
standard gold),
Hexagram (the
standard silver coin, introduced by this emperor)
Copper:
Follis, Three-Quarter
Follis,
Half-Follis,
Decanummium,
PentanummiumThere are several other mints with not as wide offerings of
denominations but other odd
types include:
Alexandria:
Copper: 12 Nummi, 6 Nummi, 3 Nummi,
NummusCarthage:
Silver:
Half-Siliqua (you might be able to get this cheaper than a
Constantinople issue), Quarter-Siliqua
Copper:
NummusRavenna:
Silver: 120 Nummi (Quarter-Siliqua)
Cherson:
Copper: 8 Pentanummia (
Follis - but with large "H" on
reverse)
Hope this helps,
Kevin