'94 achieva front end shake

I just purchased a '94 Achieva. When I test drove the care I noticed a thumping when I went over rough road. I never got the car up to highway speed. I was told by the owner that it was a strut problem. Well it turned out to be the upper right motor mount. Got it fixed. Now that it is fixed, whenever I hit 50mph I get a shake in the front end. The steering wheel shakes a little. If I push through it it stops at 60mph. I thought it might be a bad tire due to the fact that they are very old. Here is where I'm confused, When I let of the gas while at 60+ MPH it will not shake at all! I thought for a second that it might be a tranny problem, but it shifts very smooth. I got this car very cheap. Did I make a big mistake? I'm not too good with tools so please be keep that in mind.Thanks

You might try to balance your tires...although shaking in the front end is usually caused by bad tires. The car i have now had that same problem and as soon as a changed my tires got them balenced and got a front end alignment the problem went away.