The "basic" strategy for RoW is, imho, to upgrade it so much that you find your endgame equipment with it. Thus means upgdraded Tier-5 weapon and upgraded plate armor. To clarify: you find these items already upgraded. You also should hoard some scroll of transmutations because you then transmute the RoW when you no longer need it. The upgrades of the RoW scales similar as with weapons or armor. This means as wutg weapons that +1 reduces the strength requirement and then +3 again, as +6. This means the upgrades that are interesting for an RoW are +1, +3, +6, +10, +15, +22. Each if these levels may yield upgraded weapons or armor. As far as I remember (and it may have changed) a +1 RoW can drop +1 equipment, a +3 RoW can drop +2, a +6 can drop +3.

Let's assume you upgrade to +10. this should eventually drop +4 weapon and +4 plate armor and then still having +5 SoUs left to either upgrade tge weapon, the plate armor, another ring (+4 rings could drop as well). Just to finalize tbe example: We use the 5 SoUs to upgrade the weapon, then our final equipment is: +9 weapon, +4 plate (maybe the smith can upgrads to +5) and a +10 ring, that was the RoW before transmuted. This is a good enough equipment in my opinion.

So, tl;dr: +6 or +10 is what I would do. +15 for the fun of it.

A final reminder: The equipment still needs to drop, which is random. So you may just die before anything useful drops. And you need a lot of Scrolls of Curse Removal, since you usually fund a lot of stuff.

You can transmute it into something else, which I want I do after the dwarf king. Level 3-4 is the sweet spot imo. You get pretty consistent drops

As a mage, +3 is probably a fair stopping point, maybe +5 if you really want the higher end equipment. You need the upgrades for your staff.

For other classes, it depends. As a huntress, I’ll often stop at +11 or +13, depending on what level I found it at. Farming consumables and higher end equipment can be super fun! A +13 ring of wealth will provide +7 armor and weapons, which can easily be game winners. The higher level also will provide several scrolls of transmutation that I often use after dwarf king to get the ring that I want.

Went on a RoW +15 run yesterday with a Warden. After I was bored of farming I had a +8 plate (upgraded through the Smith), +6 Ring of Sharpshooting and a +7 Ring of Furor. In the end I didn't even use my +15 Ring because it wouldn't transform into anything I liked. Still had fun and almost every artifact possible.

With a mage though I always just find nice weapons I don't want to use and no armor or other useful equipment. So I usually don't bother upgrading the ring with him. RNGesus is just not with me.

TL,DR for this whole comment section: do whatever you want. You can +15 it or +15 a plate armor you find in the path, do as you wish.

I never go above +3. You will be swimming in consumables, and your other equipment needs upgrades too.