I'm about to make a campaign on my own and one of the things I want the characters to do is obtain service to an emperor in exchange for services(One of the services involves the Eye and Hand of Vecna). I'm trying to decide what order to do the services in. I need to know, how do you rank the following magic type items:
Most of the relevant aspects of magic items are covered in DMG Chapter 7 (Treasure), especially pp. 179-228. There is an explicit statement on DMG 135:
Each magic item has a rarity: common, uncommon, rare, very rare, or legendary. Common magic items, such as a potion of healing, are the most plentiful. Some legendary items, such as the Apparatus of Kwalish, are unique...Rarity provides a rough measure of an item's power relative to other magic items. Each rarity corresponds to character level, as shown in the Magic Item Rarity table.
However, there is a simple table on DMG 285 that may most directly answer your question. It shows the magic item categories ranked in both, well, power and rarity:
| Rarity | Power (Spell Level Equivalent) | Power (plus) |
|---|---|---|
| Common | 1st level spells | - |
| Uncommon | 3rd | +1 |
| Rare | 6th | +2 |
| Very Rare | 8th | +3 |
| Legendary | 9th | +4 |
"Wondrous", on the other hand, is not a ranking based on power and rarity. Rather, it is one category of item based roughly on item function, and serves to organize the random treasure tables. Equivalent categories are "armor", "wand", and so forth.
Finally, you mention The Eye and Hand of Vecna. These are artifacts, items that are "off the scale" of rarity and power. they should not be treated as simply more powerful magic items, but as things which drive the plot of the campaign itself.
DMG 219 says:
An artifact is a unique magic item of tremendous power, with its own origin and history. An artifact might have been created by gods or mortals of awesome power...Characters don't typically find artifacts in the normal course of adventuring. In fact, artifacts only appear when you want them to, for they are as much plot devices as magic items. Tracking down and recovering an artifact is often the main goal of an adventure.
Here is a question with several answers discussing the various rarity levels of items. It may also be somewhat relevant to your situation, since you seem to be trying to decide what items to, as that question puts it, "hand out".
The rarity table, copied from Dale M's answer:
| Rarity | Character Level | Value |
|---|---|---|
| Common | 1st or higher | 50-100 gp |
| Uncommon | 1st or higher | 101-500 gp |
| Rare | 5th or higher | 501-5,000 gp |
| Very rare | 11th or higher | 5,001-50,000 gp |
| Legendary | 17th or higher | 50,001+ gp |
Apart from these "ordinary" levels, there are also Artifacts or Unique items, which unlike "normal" magic items cannot be (re)created.
"Wondrous" is not a term of rarity - rather, it is a type of item, which can be of any rarity. It is basically something which doesn't fit in any other category - it isn't a weapon, armor, staff, ring, potion, rod, wand, scroll, etc.
