C++ enforcing a standard: size_t

Simple question, Would it be good for me to force myself to start using size_t (or unsigned longs?) in places where I would normally use ints when dealing with arrays or other large datastructures?

Say you have a vector pointer:

auto myVectorPtr = myVector;

Unknown to you, the size of this vector is larger than:

std::numeric_limits<int>::max();

and you have a loop:

for(int i = 0; i < myVectorPtr->size(); ++i)

wouldn't it be preferable to use

for(size_t i = 0; i < myVectorPtr->size(); ++i)

to avoid running into overflows?

I guess my question really is, are there any side effects of using size_t (or unsigned longs?) in arithmetic and other common operations. Is there anything I need to watch out for if I started using size_t (or unsigned longs?) instead of the classic int.