I know, everyone’s mileage may vary but here goes. I would probably go with the oven first, because it seems like a cheap fix, especially with a handy man in our house. I figure we could order the part and dh could fix it. Plus we need to eat and an oven is used here at our house weekly, if not several times a week.
Second, I’d go with the dryer. I cannot even imagine lugging wet clothes from one floor to another. (Thankfully we live in a single story home.) We have temporarily been without a working washer before. We would take the dirty clothes to the laundromat to wash, then lug home the wet clothes to dry them. It was a chore and I hated it. Actually I hated feeding the coins in more than anything but lugging wet clothes was a close 2nd. To me my time is worth something and all that lugging seems like a time eater. So my 2nd thing to fix, very close behind the oven, would be the dryer.
The last thing I’d fix is the dishwasher, simply because a dishwasher is totally not necessary and a total convenience. Yes, I love mine, we use it several times a week and I’d had to have it go out completely. However, if I had to do without one appliance for an indefinite period of time, it would be the dishwasher. Hand washing is an cheap, easy fix for the moment, for an extended period of time or for a lifetime. People lived without automatic dishwashers for 1000’s of years.
Anyway, that is what I’d do but everyone is different.