I'm an optometrist. I also have a little welding experience.
What works the best for one person will be completely different for another. It depends entirely on 3 things:
1. Your prescription (both for distance, and the "add" for near)
2. Your working distance (How far away your eyeball is from the weld pool)
3. The position of the work (below you? above you? etc)
My advice would be to measure your typical working distance before going to your optometrist, then let them know your concerns.
The thing to remember about glasses is that they are constant. i.e. Through one prescription, glasses will put things in focus for one specific distance; that's why you can't see far distances out of your readers. (FYI, to your optometrist, anything beyond arm's reach is considered "optical infinity," or far)
If you're looking for one pair of glasses to meet all your needs, your best bet is a PROGRESSIVE LENS (blended bifocal). You will get distance vision out of the top of the specs, near vision through the bottom of the specs, and a small area of intermediate distance (like computer or dashboard) through the middle. Keep in mind that each portion of the lens will only be clear at once specific distance, so head positioning is key. You must force yourself to wear your progressives all day, every day for 2 weeks while you adapt and teach yourself where the "sweet spots" are in your new glasses. Also note that progressives will cause peripheral distortion: you can't read out of the sides of them, the ground will seem closer than it is, and you have to remember to point your nose at what you're reading/welding so that you look through the middle of the bottom portion of the lens.
Double D's are fun

, and a great solution for people who need to do near work over their heads. (They are bifocals on top AND bottom of your lens, with the distance portion in the center.)
I hope this helps!