you can look at the coins' designs here:
https://www.ecb.europa.eu/euro/coins/html/index.en.html
https://www.eurocoinscatalog.com/
my top 10:
10)
Maltese 2€ (1€) - simplistic design
9)
Greek 2c - the ship is nice plus lepta written in Greek letters
8 )
Croatian 1€ - the marten is cute and the checkboard is also elegant
7)
Italian 10c - I like the hair and how it goes all the way into the edge 
6)
Lithuanian 2€ (all coins) - I like the coat of arms as well as the fact that the horse's legs step inside the outer edge 
5)
Slovak 2€ (1€) - another simplistic one and I like the background of the cross
4)
Finnish 1€ - swans are beautiful birds
3)
Greek 1€ - the duolingo owl is very cute 
2)
French 20c (10&50c) - the sower is beautiful and I love the lines that go to the edges of the coin which makes it stand out
1)
French 2€ (1€) - I love the tree and that the whole outer ring is covered by lines again, French design is really the best in the world 
as for the coins themselves, my favorite is 2€ and 20c
