You can use 伯,仲,叔,季 or 孟,仲,叔,季 to mean first,second,third,forth. These terms come from the ordering of siblings. The first set of 伯,仲,叔,季 is the ordering of male sibilings and 孟,仲,叔,季 is the of the female siblings.
Note that these terms are quite formal. And the original meaning of ordering of siblings is also outdated (it's like some old time Chinese custom where you have everyone's place in family hierarchy specified)
A 成語, 伯仲之間, means that two are equally matched. It means literally "between the oldest brother and second oldest brother".
But in your case, @Doubble22's answer is most appropriate. 第+number+adjective is most common expression here.
Edit#1: Also, 冠,亞,季,殿 is more common. It's widely used to refer to first place, second place, third place, and forth place in some competition. The person who got first place, second place, third place, or forth place is call 冠軍,亞軍,季軍,殿軍.
Edit#2: Also in a exam or test, first place, second place, and thrid place is 狀元, 榜眼, 探花. The origin is these are the title given to the first place, second, third in 科舉考試 (if you pass this test you get to become an government official)
Another fun thing is that you can say someone is 名落孫山 if and only if he fail at . The origin of this 成語 is that in the time of 科舉, a guy named 孫山 is the one who passed the test with worst score. So if you're behind him you've failed.