I am learning Monte Carlo and just manage to simulate a phase transition by computing the heat capacity or the susceptibility. I wish I can also compute critical exponents.To this purpose, I have read some references, especially about the finite size scaling. As far as my understanding, one of the key difficulty is that one has to be very close to the critical point to make sure he/she is in the critical region. However, I don't know how close is close enough. For example, the critical temperature of the $2d$ Ising model is known as $T_c = 2.27$. If I want compute critical exponents, is $T = 2.26$ or $T=2.28$ close enough? Put in another way, is $T = 0.99$ $T_c$ or $T = 0.999$ $T_c$ sufficiently close?

I would be very appreciate for any hints or references.