Numerical simulations of rising magnetic flux tubes in the solar convection zone have contributed significantly to our understanding of the basic properties of sunspot groups. They have provided an important clue to the operation of the solar dynamo by predicting strong (super-equipartition) magnetic fields near the bottom of the convection zone. We have investigated to what extent the simulation results (obtained on the basis of the thin flux tube approximation) depend on the assumptions made about the initial state of a magnetic flux tube at the start of the simulation. Two initial conditions used in the literature have been considered in detail: mechanical equilibrium (MEQ) and temperature balance (TBL). It turns out that the requirement of super-equipartition field strength is a robust feature of the simulations, largely independent of the choice of initial conditions: emergence of active regions at low latitudes and the correct dependence of their tilt angle (with respect to the east-west direction) as a function of heliographic latitude require an initial magnetic field strength on the order of 105 G. Other properties of rising flux tubes, such as the asymmetries of shape and field strength between the leading and following wings (with respect to the direction of rotation) of a rising loop, or the anchoring of part of the flux tube in the overshoot region, depend on the initial condition. Observed asymmetries in the magnetic flux distribution and of proper motions in emerging active regions favor MEQ over TBL as the proper initial condition. MEQ should also be preferred for other theoretical reasons: it allows for fewer free parameters, it requires no fine tuning for the tube geometry and background stratification in the overshoot region, and it can be easily made compatible with an encompassing model of the generation, storage, and eruption of the magnetic flux. We have also studied whether an external upflow (convective updraft) can trigger the eruption of an otherwise stably stored flux tube in the overshoot region. We find that a significant deformation and destabilization of a flux tube with equipartition field strength requires coherent upflow velocities of 20-50 m s-1 in the overshoot layer, which is an order of magnitude larger than current estimates for such velocities.