V-brakes eliminate the tire width issue with caliper brakes.
I’d still look for a rim with the same external width that you have now. While some, I’m not one of them, are concerned with internal width, your brakes make contact with the external surface.
Yes v-brakes are easy to adjust, and if the rims are close in width a turn of the adjuster at the lever might work, but if they are not you don’t want to have to re-set the cable every time. That will just cause it to break and fray over time.
You also want to get the cassette located the same distance from the dropout. If it is close you can use very washers washers on the axle, or behind the cassette (depending on which way it needs to move) to keep the limit screws and barrel adjuster the same.
John