The GE dryer you have (if it's electric) is a good reliable dryer for the most part.
These washers are GE's Filter-flo models. As much as I think they are cool to "play"with they are WATER HOGS.
They have a huge stationary outer tub which is where all the water is wasted. You'll use more water, more hot water, more detergent, and if you have to treat your water in a water softener and filtration system, you'll be paying more there as well. If you have to pump your gray water from your basement, you'll be paying more in electricity costs as well.
If it was just one or two people, it would be fine.
With kids who use A LOT of clothes I've heard, get yourself a good front loader. They clean better, they use 1/4 of the water that these hogs will, less detergent, they get the clothes cleaner, and if you get something new or newer, it's probably going to last you a while and you should get a warranty.
You don't know about these machines. They are about 35-40 years old. They may already have problems like an oil leak.
It's one thing for a family to be without a dryer; it's completely another to not have a reliable washer.
Best of luck to you.