You can do either. Think about it. Where you place the standard solution doesn't actually matter. For argument's sake, let us assume that we have a 0.500 M solution of HCl and an unknown solution of NaOH that is really 1.00 M.
Let us assume that first, we place the HCl in the conical flask, 20.00 mL of it. We know that we have 20 mL*0.5 L = 10 mmol HCl, so we need 10 mmol NaOH, which if it was actually 1.00 M, we would need 10.00 mL of it.
Now let's reverse things. If we have 20.00 mL of NaOH in the conical flask and titrate this, we have 2 mmol NaOH needing 40.00 mL HCl. In either case, as all we have changed is what is titrating what, the concentrations of the respective solutions cannot change. Therefore, it does not matter what you place in what. The calculations will still work out. Just make sure that your rinsing follows accordingly.