First of all, are you serious about stepping in? Would you mind to tell us if the girl is a normal girl or a girl from those "fun place"...
I will call it sinking if she is from "fun place", and my recommendation is... consider, re-consider and re-re-consider again!!
Sinking is always not recommend if you are newbie...
For rent a house... if your budget is tight... you could only got some "民房" and the price is approx $1000- $1900... depends on location and size... but you got to take care of the security issue as it is very normal to have "爆格"...
On the other hand, if you want to have high security with HK Style estate management... those apartment cause $2500-xxxx" depends on size and location too...