Pages of the innodb data files get cached in the innodb buffer pool. This is what you'd expect. Reading files is slow, even on good hard drives, especially random reads which is mostly what databases see.
It may be that your first query is doing some kind of table scan which pulls a lot of pages into the buffer pool, then accessing them is fast. Or something similar.
This is what I'd expect.
Ideally, use the same engine for all tables (exceptions: system tables, temporary tables (perhaps) and very small tables or short-lived ones). If you don't do this then they have to fight for ram.
Assuming all your tables are innodb, make the buffer pool use up to 75% of the server's physical ram (assuming you don't run too many other tasks on the machine).
Then you will be able to fit around 12G of your database into ram, so once it's "warmed up", the "most used" 12G of your database will be in ram, where accessing it is nice and fast.
Some users of mysql tend to "warm up" production servers following a restart by sending them queries copied from another machine for a while (these will be replication slaves) until they add them into their production pool. This avoids the extreme slowness seen while the cache is cold. For example, Youtube does this (or at least it used to; Google bought them and they may now use Google-fu)
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