Shaking while you brake is associated with warped front-rotors. A trusty mechanic can install rotors + brakes for $150 a side tops. You can do it yourself for less than $70 a side.
Shaking assiciated with highway driving is usually caused by alignment issues or unbalanced tires. Alignments usually cost $150-$200. Sometimes you can get a free alighnment if you buy new tires (since you're at 60,000 miles it might be worth it). And wheel balancing is cheap and should be done when you get new wheels.
If it were my car, I would buy new tires (assuming the old ones are worn) and while the mechanic is switching them out, have him install new rotors (and probably brakes). When the wheels are on, balance and align them -
$500 tires
$150x2 rotors+brakes
$200 alighnment + balance
$1000 Total bill