There is a difference between British and American English here.
In British English, you could use any of those words in this sentence. However, 'hire' would suggest a shorter period - for example hiring out a room for a day or a few hours, for example for a party or a meeting. Rent or let out, by contrast, is for a longer period : you'd rent or let out space to tenants who would either live or work in a space for several months or more.
I hope an American English speaker can tell you more about the US Eng usage.