Should I use utf8_unicode_ci or utf8_slovak_ci?
I am not going to answer you because I do not know utf8_slovak_ci nor the slovak language, but I will tell you how I would test it myself:

Take an extensive list of words containing "problematic" (as in, non-existant in the English alphabet) letter representations (as far as I know, letters in your language containing ˇ, ´, ¨ and ˆ, maybe others)- Please forgive my ignorance of your language.

Sort them and compare them using the 2 potential collations, like this:

SELECT word FROM test_table ORDER BY word COLLATE utf8_slovak_ci;
SELECT word FROM test_table ORDER BY word COLLATE utf8_unicode_ci;

SELECT word FROM test_table WHERE word like 'ž%' COLLATE utf8_slovak_ci;
SELECT word FROM test_table WHERE word like 'ž%' COLLATE utf8_unicode_ci;


Check for differences between them, and with the common orthography rules.

If you get similar results, they should be equivalent, and you should think whether you want to also use the collation rules of the other languages (even if your site is only Slovak, I may register there as "jynus from Logroño", which contains a "problematic" character). In that case, use the unicode version, and remember that at any time you can change the collation of comparisons for particular queries. For example:

mysql&gt; SELECT 'a' = 'á' COLLATE utf8_unicode_ci, 'a' = 'á' COLLATE utf8_bin;
+------------------------------------+-----------------------------+
| 'a' = 'á' COLLATE utf8_unicode_ci  | 'a' = 'á' COLLATE utf8_bin  |
+------------------------------------+-----------------------------+
|                                  1 |                           0 |
+------------------------------------+-----------------------------+
1 row in set (0.01 sec)