For educational purposes, you are going to want to mostly stick to larger coins (5-8mm Greek silvers are extremely difficult to find when dropped on the carpet... ask me how I know that) the Romans made some terrific bronzes, but except for Ptolemaic egypt, you will probably want to stick to silver for Greek.
Some recommendations that are impressive, but won't break the bank:
Greek:
1) Miletos silver 1/12 stater, c. 500 BC ($20-50)

These are by far the most affordable and attractive coins struck prior to 499 BC. They are believed to have been made to pay mercenaries in a rebellion against the Achaemenids; the city was razed to the ground in 499.
2) An attractive silver obol from the Classical period. Tie it in with the lesson that "obol" was a cooking spit - a necessary commodity that could be traded. A drachm (from ΔPAΣΣOMAI, "To Grasp") was worth six obols; the number an adult male could typically hold in a closed fist. I have a fondness for the obols of Kyzikos, which are common, charming, and inexpensive:

3) A coin of Alexander the Great. You can get a medium-medium-high grade drachm for $40-100, or a lower grade tetradrachm for about $100-150

4) A coin of the Seleucid Empire. Lower grade tetradrachms are affordable in reasonable grades; typically not more than 200 until you hit high grades or rare rulers. Here is mine of Antiochus I Soter:

5) A nice, big bronze of Ptolemaic egypt. These come in sizes from about 9mm all the way up to nearly 50mm! Coins in the 32-38mm range are more affordable ($20-50) in middle grades.


Rome:
1) A nice big early anonymous As (Can be bought for around $50)

2) Any coin of Augustus (As little as $5 up to thousands)
Small bronze with his client king Rhoemetalkes - cost less than $30

3) Any other coin of the golden age - even high grade denarii can be quite affordable, although sestertii (bigger than half dollar size) are better for passing around
Nero ($150)

Trajan ($50-100)

Hadrian ($50-100)

Antoninus Pius

Marcus Aurelius ($50-100)

4) I would do a couple coins from the Crisis, 238-284. Antoninianii were the primary coin of that time, and the rapid debasement of the 250s was striking. Here are two coins of Gallienus; left is about 20-25% silver, left is debased to something like 3-8%. Go for a Gordian III antoninianus, they are only $30-40 even in mint state. Debased antoninianii are only a dollar or two.

5) A nice big follis of the Tetrarchy, can be had typically for $20-50 in high grade:

6) A coin of Constantine the Great is a must!
7) A tiny AE4 from the end of the empire - Honorius or any of the later Eastern emperors can be had for between $1 and $100, depending in rarity
Zeno, emperor of the East when the West fell to Odoacer
