'What's that building?'
In Polish it's exactly that: "Co to za budynek?" It's a perfectly normal sentence. One could add "jest" ("Co to jest za budynek?"), but I'm guessing that many people in fast, everyday speech would just say "Co to za budynek?". It's shorter, faster. It's like "What's that building?" versus "What is that building?"
when there is a more precise and correct way of enquiring which is to say 'jakiego typu/rodzaju?'
Yes, this is more precise. So, "Jakiego typu/rodzaju to budynek?" would fit, for example, only "a semi-detached house" and maybe "a brick building" (although Poles would usually ask in this case "Z czego jest zbudowany ten budynek?").
You can also ask "Co to za typ/rodzaj budynku?"
And in other cases:
a) a post office
"Co to za budynek?"
If someone inquired about a post office building by asking "Co to za typ/rodzaj budynku?" my first thought would probably be "budynek użyteczności publicznej" (public building) lol So, in my opinion it's better to just ask "Co to za budynek?"
b) an example of early 19th century architecture
"Z jakiego okresu jest ten budynek?" (what period) or "Z którego wieku jest ten budynek?" (which century).
I think that asking about "typ/rodzaj" would make sense if the answer was "kamienica z XIX wieku" ("a tenement house from the 19th century").
And jon357 is right - "Co za budynek!" ("What a building!") is an exclamation, something completely different than "Co to za budynek?". Although I can imagine such use in a very colloquial, sloppy speech. For example, one guy says that his friend saw some spooky, haunted building, but his friend gets embarrassed and upset and claims that he didn't:
- Adam powiedział, że widział wczoraj jakiś nawiedzony budynek na wzgórzu!
- Co za budynek znowu? Gdzie? Wcale nie... Żadnego budynku nie widziałem.