Sorry for the horrible photo, smartphone camera + overhead lamp + shaky hands =/= good photography.
(This was the best of about 50 attempts. Most of the time, the top row was a bunch of unidentifiable smudges.)
I'll try to make a better photo later (and also include some of my other types that I couldn't find quickly enough).
Maybe it should be done as a series of photos - there's simply too many coins (somewhere in the vicinity of 35-40 - this photo has 30 but it's missing a few).

Top row (wire kopeks):
1. Ivan IV sword kopek, ca. 1535
2. Ivan IV regular early kopek, ca. 1535-47
3. Ivan IV Novgorod? early kopek, ca. 1535-47?
4. Feodor I kopek, ca. 1586-98
5. Feodor I dated kopek, 1597
6. Boris undated kopek, ca. 1598-1605
7. Boris dated kopek, 1599
8. Michael kopek (double struck?), ca. 1613?
9. Swedish Novgorod kopek, ca. 1615-17
10. Peter I early dated kopek, 1700?
Second row:
11. Peter I copper kopek, 1713
12. Cross kopek, 1728
13. (2 kopek 1757 struck over) cloud kopek, 1750s
14. Elizabeth kopek, 1760
15. Siberian kopek, 1768
16. Catherine II kopek, 1789
Third row:
17. Paul I kopek, 1798
18. Eagle? kopek, 1830
19. Masonic kopek, 1832
20. Kopek in silver, 1840
21. Nicholas I crown kopek, 1854
22. Alexander II crown kopek, 1855
Fourth (bottom) row:
23. Late empire kopek, 1883
24. Soviet proletarian kopek, 1935
25. Soviet 7 ribbon kopek, 1936
26. Soviet 11 ribbon kopek, 1946
27. Soviet 16 ribbon kopek, 1952
28. Soviet 15 ribbon kopek, 1957
29. Soviet post-reform kopek, 1972
30. Modern kopek, 1997
Notably absent (but I actually have):
- Ivan IV post-1547 kopek (my only example is in a 2x2)
- Copper Revolt kopek
- Ivan V kopek
- Peter I undated kopek (OK, not sure if I have one)
- Peter I "Russia" kopek
- Peter I late (post-1700) dated wire kopek
- the large 1924 Soviet kopek
- maybe others
Should also be there for reasonable completeness:
- any Novgorod denga of kopek size (very uncommon)
- False Dmitry (uncommon)
- Vasily (uncommon)
- Vladislav (rare)
- Alexey silver
- Feodor III (very uncommon)
- non-overstruck cloud kopek (uncommon)
- ring kopek of Alexander I (rare)
- I probably forgot something
Note: most of those coins were bought in 2010-12, in the early days of my collecting, and are of rather awful quality.
However, the coins in the right half of the second row are actually much better in hand - it's the photo that made them smooth, they're just very dark and not very contrasting (though the 1760 kopek
is quite worn).
Bonus factoid: as far as I can tell, the coin in the upper right corner is the holder of a significant record over the entirety of numismatics. What do you think this record is?