Cheapest fix - add some air to the front tyres - at least 2psi higher than the rears. That will reduce the tendency for understeer. Maybe add air to the rears as well, but always have higher pressure in the fronts.
Then, fit a heavy duty rear sway bar. That will further reduce the understeer.
Then heavyduty springs all round.
IMO, you don't need "coilovers", just a simple upgraded shock - KYB, Tokico, Bilstein. "Coilovers" are generally fully height adjustable, and are usually installed so that the weight can be distributed evenly across the suspension. If not set up correctly your car will probably handle even worse than it does now.