Spongy brake fix?

im reading about bleeding the MC right. well the car i just bought has this problem. The brakes go down real far before the give pressure. Especially at low speeds. the faster i go, they kinda feel a little better. another thing is under hard braking the steering wheel shakes pretty bad. my thoughts are maybe the one way valve for the brake booster. or just need to be bled. the master cylinder looks brand new. and i think it was done at a rinky dink gas station. any thoughts/suggestions?