struts or shocks ???

I bought a 93 I4 auto (at auction) when I drove it off the lot I knew I was going to be challenged. The car drove like a tank when I hit the brakes I jumped and shuddered so bad. I almost got out and ran. I put new brake rotors,bearings seals and pads. That appears to have corrected the braking problem. Now..... suspension, with the car parked I can push on the drivers fender and it gives (a little travel) when I push on the passenger side no travel solid as a rock (no travel). Its a terror to drive every bump can be felt throughout your body. Much like a buckboard would ride I assume. I've been told its the struts and I've been told it's the shocks because it has no travel?? anyone have any Ideas. Car looks great in and out. runs excellent I was told mileage was 111,800 but who knows? I really could use some input.

thanks I was able to find and order 2 monroe struts for 31.53 each /free shipping. Due to the information furnished by assistant